"He has not been cleared by our doctors to play in rehab games yet," GM Brian Cashman told ESPNNewYork.com on Monday, refuting a report in a New York newspaper that Rodriguez had been cleared and would begin playing rehab games with the Class A Tampa Yankees on July 1.
"He's getting closer, there's no doubt about it, but we don't have a date for him to start playing games yet," Cashman said. "It could be July 1. It could also be July 5, or maybe June 25."
Once a position player officially begins a rehab assignment, an organization has 20 days to promote him to the major leagues or option him to a minor league affiliate. If all proceeds on schedule, that means Rodriguez could rejoin the Yankees shortly after the All-Star break.
Rodriguez continued taking simulated at-bats Monday at the Yankees' minor league complex in Tampa, Fla., hitting a ball to the base of the center-field fence and another to the warning track in left center off a minor league right-hander.
"He's taking batting practice, he's running, he's doing fielding drills," Cashman said. "He's doing everything we need to see him to do progress to the next step. But I have not had a conversation with anyone about when his rehab clock would start."
In sessions late last week, A-Rod primarily hit grounders mixed in with a couple liners. Rodriguez also had an extensive baserunning session Monday and did sliding drills on a mat in the outfield.
Rodriguez underwent surgery to repair a torn labrum in his left hip in January. The Yankees signed Kevin Youkilis to a one-year, $12 million contract to hold down A-Rod's position until he returned, but Youkilis has been injured for much of the season. Last week Youkilis underwent surgery for a herniated disk in his lower back that is likely to finish him for the season.
In their absence, the Yankees have cobbled together their third-base job with a combination of journeymen Chris Nelson -- who has since been released -- Jayson Nix and rookie David Adams. Veteran outfielder Vernon Wells has also been pressed into duty at third base in one game.
The return of Rodriguez would help solve that problem for the Yankees, who are currently in third place in the AL East with a 41-34 record, 2½ games behind the Boston Red Sox.
"We haven't had our real team all season, so it's hard to judge us," Cashman said. "But obviously, we're within striking distance regardless of everything that's happened, so we're thankful for that."
Jeter had relocated his rehab Saturday and Sunday to Yankee Stadium. Jeter hasn't played this season after breaking his ankle in the ALCS opener Oct. 13. After surgery, he played just five spring training games because of soreness. A new break was discovered April 18.
Nunez, who strained a muscle on his left side while filling in for Jeter at shortstop, also took simulated at-bats, ran the bases and did slides with Rodriguez.
Information from The Associated Press was used in this report.