Curtis Granderson was the first one back from the disabled list and it appears Mark Teixeira will be the second, with Kevin Youkilis a close third.

“He could start a rehab [assignment] Tuesday in Trenton [Double-A],’’ general manager Brian Cashman said yesterday after Teixeira worked out at the Yankees’ minor league complex. “Hopefully, everything continues to go right for him and in the first week of June he will be ready for us.’’

Teixeira has not played this season due to a tendon problem in the right wrist suffered March 5 while part of the United States’ World Baseball Classic team.

Lately, he has been participating in simulated games instead of playing in extended spring games because he can see more pitches in the controlled atmosphere of simulated games.

Yesterday, Teixeira and Youkilis took batting practice on the field at the complex.

While Lyle Overbay has filled in very well for Teixeira and became the full-time first baseman when Youkilis went on the DL with a lower back problem late last month, Teixeira represents an upgrade over Overbay, who has started 21 of 22 games since Youkilis last played on April 27 and is hitting .250 with seven homers and 25 RBIs.

One area of concern with Overbay, who wasn’t supposed to face lefties because Youkilis was set to play first against them, is batting .140 (6-for-43) versus left-handers.

Teixeira’s return doesn’t mean Overbay will be jettisoned. The Yankees have to be sure Teixeira’s tendon problem doesn’t resurface, because if it does and Overbay, who would be picked up immediately by another team if let go, is gone, the Yankees don’t have a first baseman at least until Youkilis returns.

“Everything’s great. I can’t be happier with how I feel,” Teixeira said. “Taking at-bats, playing in a few more games here and hopefully next week go on a rehab assignment at some point.”

Trenton starts a three-game series against Erie at home Tuesday.