According to the report, which was posted Saturday morning on SI.com, sources told the publication that Rodriguez was on a list of 104 players who tested positive that year, when Major League Baseball conducted survey tests to see if mandatory, random drug-testing was needed.
Sources who know about the testing results told Sports Illustrated that Rodriguez tested positive for testosterone and Primobolan, an anabolic steroid.
In 2003, there were no penalties for a positive result.
Rodriguez, reached at a Miami gym Thursday for comment by Sports Illustrated, said: "You'll have to talk to the union."
Asked if there were an explanation for the positive test result, Rodriguez told SI: "I'm not saying anything."
Sources confirmed to ESPN that Rodriguez, now with the New York Yankees, was aware he tested positive for steroids in 2003.
Primobolan, also known as methenolone, is an injected or orally administered drug. It improves strength and maintains lean muscle with minimal bulk development and few side effects. It is not an approved prescription drug in the United States. Testosterone can be taken legally with a prescription.
In a December 2007 interview with "60 Minutes," however, three days after George Mitchell's report on drugs in the sport was released, Rodriguez denied using performance-enhancing drugs.
"I've never felt overmatched on the baseball field. ... I felt that if I did my, my work as I've done since I was, you know, a rookie back in Seattle, I didn't have a problem competing at any level," he said on "60 Minutes."
Mitchell said his report included names of players who he "had received credible evidence of their illegal purchase, possession, or use of performance enhancing substances." Rodriguez's name was not included.
"I did not have access to the results of the 2003 drug testing, and to this day I do not know which players tested positive then," Mitchell said in a prepared statement Saturday night.
Yankees general manager Brian Cashman said: "At this stage, we have no comment."
Rangers general manager Jon Daniels, who was assistant of baseball operations with the team in 2003, told The Dallas Morning News that the notion of Rodriguez using steroids during that season "was not a topic of conversation."
"This SI report is the first I've heard of it [Alex Rodriguez's test]," Daniels told the newspaper.
Rodriguez's agent, Scott Boras, who spoke with ESPN's Karl Ravech, said he would not have any official statement and will wait to see what Rodriguez wants to do.
Boras said he has no knowledge of any positive tests for Rodriguez.
The Major League Baseball Players Association issued a statement Saturday afternoon: "Information and documents relating to the results of the 2003 MLB testing program are both confidential and under seal by court orders. We are prohibited from confirming or denying any allegation about the test results of any particular player[s] by the collective bargaining agreement and by court orders. Anyone with knowledge of such documents who discloses their contents may be in violation of those court orders."
Major League Baseball said it was "disturbed" by the report, but did not elaborate because of player confidentiality.
"Because the survey testing that took place in 2003 was intended to be nondisciplinary and anonymous, we cannot make any comment on the accuracy of this report as it pertains to the player named," MLB executive vice president Rob Manfred said.
Survey testing was created in 2003, in an agreement with the MLBPA, to see if mandatory testing and penalties needed to be implemented in 2004 -- it also was specifically designed to ensure players would not be identified.
The actual samples of 1,198 players were kept in one lab in Las Vegas and had codes, not players' names. A list with the names and corresponding codes was in an office in Long Beach, Calif. They were never supposed to be united.
MLB and the union had a deal with the company that any negative samples were to be automatically destroyed after 30 days. However, because of the current Barry Bonds investigation and the evidence the government is seeking to present in his current perjury case, it is now known that samples were not destroyed.
Federal agents, with search warrants, raided the labs in April 2004, looking for the 2003 results of 10 players believed to be linked with their BALCO investigation. In their search, however, investigators came upon the full list of 104 players -- which reportedly included Rodriguez's name.
Shortly thereafter, the union notified the 104 players whose samples were seized that they had tested positive.
Rodriguez has never been linked to the BALCO case.
But, former slugger Jose Canseco did link Rodriguez to steroids in his book "Vindicated."
"I said in my book 'Vindicated' that he was a known steroid user before 2000," Canseco told the Miami Herald. "It's old news. I've been saying this forever. You guys are playing catch-up."
The publisher of Canseco's first book, "Juiced," deleted references to Rodriguez because Canseco had not witnessed Rodriguez using steroids, Canseco's former lawyer, Rob Saunooke told the Los Angeles Times. References to Rodriguez were included in Canseco's second book, "Vindicated," after Canseco passed a lie detector test with questions about Rodriquez's alleged steroid use, Saunooke said.
Sports Illustrated also reported that according to three big league players, Rodriguez in September 2004 was tipped off by union chief operating officer Gene Orza that he would be tested later that month. SI asked Rodriguez about the allegation, but he declined to comment.
Orza, according to the 2007 Mitchell report, had violated the union's agreement with MLB by informing a player about an upcoming drug test. The player was not identified in the report.
SI questioned Orza on Friday about the tipping allegations, and Orza responded: "I'm not interested in discussing this information with you."
The union statement on Saturday also addressed the allegations. "As we have explained previously, in detail and in public, there was no improper tipping of players in 2004 about the timing of drug tests."
More than 5 percent of players in the majors tested positive for performance-enhancing substances in the '03 survey, and mandatory testing was implemented -- including provisions for penalties -- in 2004.
Even if Major League Baseball were to confirm that Rodriguez was one of the players to test positive in 2003, he would not be subject to any sort of discipline based on that testing.
However, if information emerges about positive tests from 2004 on, circumstances could change. There have been players connected with HGH purchases from 2004 and forward, for example, who have been subject to discipline by the commissioner's office.
"I think in the climate that we have today, you don't have much shock anymore," Rangers senior adviser John Hart said on the MLB Network. Hart was the general manager in 2003. "Obviously Alex probably is the best player in baseball. This has always been a special talent and the guy has been putting up Hall of Fame numbers since the day he showed up in the big leagues. I've been in the game for almost 40 years and it hurts a little bit, if in fact this is true."
Rodriguez played for the Rangers from 2001 to 2003. He was traded to the Yankees in 2004. He is drawing a major league-high $27 million salary after signing a record $275 million, 10-year contract with New York in 2007.
Fernando Montes, a former director of conditioning for the Rangers, told ESPN that Daniels asked him if he suspected Rodriguez was using steroids in 2003.
Montes said he had no direct proof, but added: "Without a doubt, though, this was more than an educated guess." Montes said Daniels had no direct knowledge of Rodriguez using steroids, only what Montes told him.
Reached by ESPN, Daniels said: "I have no recollection of that conversation."
Hart pronounced himself saddened by the Sports Illustrated report.
"It breaks my heart for the game that we have this kind of thing occurring,'' he said. "But at the same time, a lot of people seem to have been caught in this net.''
Ronny Paulino, who is on the Dominican Republic team's provisional roster for the World Baseball Classic with Rodriguez, said that despite the report, he hopes A-Rod remains on the squad.
"The class of baseball player he is, anybody would want him on their team. He's the best player in baseball. Having him on the [Dominican] roster is a tremendous help. He is the best third baseman in the game," Paulino told ESPN The Magazine's Jorge Arangure.
Information from The Associated Press, ESPN.com's Jerry Crasnick, ESPN.com's Mike Fish, ESPN The Magazine senior writer Buster Olney, ESPN's T.J. Quinn, ESPN's Willie Weinbaum and ESPN The Magazine's Jorge Arangure was used in this report.