"We've had no discussions about when his rehab date will start," Yankees general manager Brian Cashman said on Monday. "He's going in the right direction. He's doing everything necessary.
"We're not in a position where anybody has had any conversation with me about getting ready to start his rehab clock. I think he's getting close; closer every day as long as he has no setbacks."
The New York Daily News, citing a person close to Rodriguez, reported on Monday that the three-time American League Most Valuable Player would begin playing for Tampa on July 1. Cashman said that report was inaccurate.
Rodriguez has been working out at the Yankees' complex in Tampa and continued taking at-bats against live pitching on Monday. Rodriguez hit 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, according to The Associated Press.
A-Rod also had an extensive baserunning session and performed sliding drills on a mat in the outfield, which represent two key steps for a player about to make the leap into playing live games against professional competition.
If healthy, Rodriguez would represent a boost for a Yankees club that would welcome contributions at third base. Kevin Youkilis signed a one-year, $12 million deal to serve as A-Rod's replacement but played in just 28 games before undergoing surgery to repair a herniated disk in his back.
Rookie David Adams is currently being given a chance to play every day at third base, and the Yankees have also looked at Jayson Nix, Chris Nelson and -- for one inning -- outfielder Vernon Wells as fill-in third basemen this season.
Rodriguez batted .272 with 18 home runs and 57 RBIs in 122 games for the Yankees last season before struggling in the postseason against the Orioles and Tigers, managing three hits in 25 at-bats.
Also on Monday in Tampa, Yankees captain Derek Jeter took batting practice with A-Rod and rehabbing infielder Eduardo Nunez. Jeter traveled to New York over the weekend and watched Sunday's Old-Timers Day ceremonies from the dugout, while also fielding ground balls on the diamond at Yankee Stadium.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.