The Red Sox have received permission from Major League Baseball to negotiate with Gonzalez on a new contract, the sources said.
The team flew in Gonzalez, who had surgery Oct. 20 on his right, non-throwing shoulder to clean up the labrum, for a physical examination Saturday. While there was no official word on the physical, a team source told ESPNBoston.com's Joe McDonald that Gonzalez "looked good."
The Red Sox continued Saturday night to work on a long-term contract with him, a source, who indicated that the negotiation window will close at 2 p.m. ET on Sunday, told ESPNBoston.com's Gordon Edes.
Sunday's deadline came and went with no new information on the deal.
"There is not a contract agreement," John Boggs, Gonzalez's agent, said Sunday afternoon, as quoted in the San Diego Tribune. "I'm right in the middle of a meeting right now, I'll get back to you. We're still working."
In exchange, the Padres would receive three prospects in pitcher Casey Kelly, first baseman Anthony Rizzo and outfielder Reymond Fuentes, according to a baseball source. The Padres also would receive a player to be named later, a source told Edes.
"He's at the peak and prime of his career, which is going to be great," said Padres first-base coach Dave Roberts, a former Red Sox player and teammate of Gonzalez in San Diego. "I've talked to him numerous times about my experience in Boston, and I knew if this opportunity did present itself, he would be very excited to be a Red Sox. I think a lot of him as a player and as a person. Boston is going to be an amazing experience for him."
Sources told Olney it's very possible the Gonzalez deal would mean the end of Adrian Beltre's time with the Red Sox, because although Kevin Youkilis could move to left field, Boston's preference probably would be to shift Youkilis to third base.
"I'm not worried about that," Youkilis said Saturday when reached by ESPNBoston.com. "I just have to work hard like I always do, and focus on playing third and not first. There's a lot of time at spring training to do all that. I'll prepare myself the right way to play as many games as I can at third base."
Gonzalez is the Padres' most popular player with great crossover appeal to the team's Mexican-American market, a native son who carried San Diego to within a game of a playoff spot in 2010.
He is signed through 2011 at $6.3 million. The Padres exercised his 2011 option Nov. 1. His contract called for a $5.5 million salary, but performance bonuses pushed the figure above $6 million.
Acquiring Gonzalez, while signing one of two free-agent outfielders, Carl Crawford or Jayson Werth, would give the Red Sox their most potent offensive lineup since the Manny Ramirez trade to the Dodgers in 2008 and make clear why they were willing to lose free agents Victor Martinez and potentially Beltre.
"It's great," Youkilis said of the Gonzalez deal. "The way he hits at Petco, he can hit at Fenway Park because he can use the [left field] wall to his advantage. It's going to be great to have him on the team. That'll be a huge acquisition for us if everything works out."
Kelly, 21, is considered the top prospect in the Red Sox organization by ESPN Scouts Inc.'s Keith Law , though the pitcher struggled a bit in his first season at Double-A in 2010. He was 3-5 with a 5.31 ERA in 21 starts for the Portland Sea Dogs, and had a 6.75 ERA in four starts in the Arizona Fall League recently.
Rizzo, also 21, had 20 homers and 80 RBIs with the Sea Dogs this past season and had an .815 OPS. He was ranked the No. 3 Red Sox prospect by Law.
The 19-year-old Fuentes was Boston's top pick in the 2009 draft. He hit .270 with 59 runs scored and 42 stolen bases in 104 games for Class A Greenville last season. He's ranked the No. 10 Red Sox prospect by Law.
The Red Sox have long coveted the 28-year-old Gonzalez. As far back as the 2009 trading deadline, the Red Sox made a pitch for Gonzalez, a three-time All-Star who last season finished fourth in balloting for the National League's Most Valuable Player.
The 6-foot-2, 225-pound left-handed hitter batted .298 with 31 home runs and 101 RBIs for the Padres last season. He finished fifth in the National League in on-base percentage (.393), ninth in slugging (.511) and first in hitting with runners in scoring position (.407).
Opposing pitchers issued 35 intentional walks to Gonzalez last season, a number exceeded only by Albert Pujols.
In addition to his offensive prowess, Gonzalez is a gifted defender, having won two Gold Gloves in five full seasons.
Gonzalez grew up in the San Diego area and was the No. 1 overall pick by Florida in the 2000 amateur draft. The Padres obtained him in a trade with Texas before the 2006 season.
While many had expected Gonzalez to be traded before the deadline last summer, the Padres were surprise contenders in the NL West and had to keep the slugger.
The Padres went 90-72 despite opening the season with a payroll of $37.8 million, second-lowest in the majors. San Diego was in contention until the final day, when its loss at San Francisco, coupled with Atlanta's win over Philadelphia, eliminated the Padres from the NL West and wild-card races.
In five seasons with San Diego, Gonzalez has 161 homers -- two shy of Nate Colbert's club record -- and 501 RBIs. Including parts of two seasons with Texas, he has 168 homers and 525 RBIs.
He set a Padres record with his fourth 30-homer season. His third 100-RBI season tied Phil Nevin for the most in club history.
The Padres already have lost right-hander Jon Garland, shortstop Miguel Tejada and catcher Yorvit Torrealba to free agency, and won't re-sign outfielders Scott Hairston and Tony Gwynn Jr. They also declined to pick up right-hander Chris Young's $8.5 million option.
Information from ESPN The Magazine's Buster Olney, ESPNBoston.com's Gordon Edes and Joe McDonald, and The Associated Press was used in this report.