With Alex Rodriguez, Derek Jeter and Mark Teixeira sidelined indefinitely, Yankees president Randy Levine didn’t rule out adding payroll if the team decides it needs help to stay in contention.

“We’re the Yankees,” Levine said before a 4-3 victory over the Rangers Tuesday night at the Stadium. “We’re always active. We’re always trying to get better.”

Levine wouldn’t get into specifics, but echoed owner Hal Steinbrenner’s idea of getting payroll under the luxury tax threshold of $189 million next season.

“Hal has said it over and over again: He’s committed to bringing a championship team to the Yankees,” Levine said. “We’ve been acting the same way for decades.”

Unlike when Teixeira initially injured himself training for the World Baseball Classic, the Yankees are on the hook for his salary, since he returned last month.

“Obviously, we have our own insurance on [Teixeira],” Levine said, regarding potential season-ending surgery. “We’ll deal with that if and when it happens. We have pretty good coverage on him, as with a lot of our players.”

Teixeira’s bothersome right wrist was examined yesterday, but the Yankees didn’t release the results.

In the meantime, they will try to survive, likely without Rodriguez, Jeter, Eduardo Nunez and Francisco Cervelli, through the All-Star break.

“You wouldn’t think so,” manager Joe Girardi said of getting any of the sidelined Yankees back by the break. “We have 20 days, and guys aren’t ready to play in rehab games [yet]. Some haven’t even done simulated games. My thought is, probably not.”

The future appears just as cloudy for Teixeira, who returned for 15 games before experiencing soreness that forced him from a June 15 game in Anaheim. A cortisone shot the next day did not alleviate the problem.

“I am concerned,” Girardi said. “I said before, it’s tricky. What he had was a tricky injury and I am concerned about it.’’

After getting off to a decent start upon his May 31 return, Teixeira quickly faltered at the plate, especially from the left side.

* Girardi isn’t going to employ six starters to get him through the entire 20 games-in-20 days stretch the Yankees began last night. It’s the longest such stretch of the season.

Nevertheless, Girardi said he will use a six-man rotation once, in order to get Ivan Nova a start.

“I’m not taking anyone out of the rotation, but we’re in a long stretch so it’s possible we might put him in there to give the guys an extra day that way,’’ Girardi said of Nova, who threw well Sunday against the Rays after being recalled from Triple-A Scranton/Wilkes-Barre.

“I’m not saying we would go to a six-man rotation the whole time. It would be just that one time so they’re not going three or four turns on five days’ rest.’’

Girardi said Nova, who allowed three runs and seven hits in 6 2/3 innings Sunday, wasn’t available in the bullpen Tuesday night, tonight and, more than likely, tomorrow.

However, Girardi said afterwards Nova could work in relief.

“If we got in a situation where I needed to use him I would use him,’’ Girardi said. “We’ll keep him in the bullpen in case of an emergency. There’s no exact plan.’’

Nova threw a bullpen session yesterday.

“I’m going to keep working like I’m pitching in five days,’’ Nova said. “Everybody I talked to liked the way I pitched.’’

* Tigers manager Jim Leyland, who will guide the AL All-Star squad next month at Citi Field, told reporters Mariano Rivera will work the ninth inning if the AL has a lead.

Some voices called for Rivera to start the game or pitch in the early innings as a tribute to his final season — an idea Rivera didn’t embrace.

“He took me off the hook from all that silly stuff that they wanted him to start the game,’’ Leyland said. “I hope I give him the ball in the ninth inning in New York.”

It’s not often the Yankees’ manager has to make sure a young player doesn’t lose confidence but remains in the lineup regularly.

Nevertheless, that’s where Girardi finds David Adams, who started at third base for the sixth time in seven games despite being buried in a 1-for-18 slump and batting .191 (17-for-89) in 26 games since being recalled from Triple-A on May 15, his 26th birthday.

“Any time it’s a young kid, you get a little bit concerned,’’ Girardi said when asked if Adams losing confidence could be a worry. “Our job is to show that we have confidence in him and that he is capable of doing this. As a young kid, you have to make adjustments.

“It’s amazing how quick they make adjustments on you, and he’s trying to do that.’’

Adams, who went 0-for-3 (all Ks) with a walk last night, says his confidence has not dipped.

“I’m struggling right now, but everyone struggles in life in anything they do,’’ said Adams, who explained he has found some mechanical flaws in his swing that needed to be corrected.

Derek Jeter is 39 today. It’s the second time Jeter has celebrated a birthday while on the disabled list. The last time was 2011. This marks the sixth time since 1996 Jeter will not play a game on his birthday.

Reid Brignac will become a free agent instead of accepting an outright assignment to Triple-A. Brignac was designated for assignment last Friday.