TAMPA — If the Yankees want to keep Aaron Judge in pinstripes for the rest of his career before he hits free agency, time is running out and Judge is bracing for a battle.

While the two sides failed to come to terms on Tuesday to avoid arbitration, Judge said the idea of an extension did come up by the Yankees — though no numbers were discussed.

Asked if he was “optimistic” a deal could be struck before Judge’s own deadline of Opening Day — which he doesn’t want to negotiate beyond — Judge said, “I’m optimistic, but it’s a short window. We’ll see what happens.’’

If they wind up battling in arbitration, there’s no telling what might happen, as Judge learned when Dellin Betances went through a particularly ugly battle with the team that became public in 2017, when he lost his arbitration case.

“I think both sides want to avoid getting into that situation, having to go into that room and have to fight each other a little bit and bring out the boxing gloves,’’ Judge said at Steinbrenner Field. “I’m prepared for it. I kind of learned back then when Dellin went through it, I talked to him about that process and got a heads up about how that works. And I think our team is prepared for it and ready for it.”

The two sides filed numbers for 2022 on Tuesday, with Judge filing for $21 million and the Yankees countering with $17 million.

Due to the length of the MLB lockout this offseason, arbitration hearings will be heard during the regular season.

“I’m not too happy about an arbitration hearing being on a date … [when] we’re playing in a game at 7 [p.m.] and having to be in a courtroom at 10 a.m,’’ Judge said.

Before that happens, Judge remains open to the idea of keeping the lines of communication open.

Both managing general partner Hal Steinbrenner and general manager Brian Cashman have praised Judge leading up to the negotiations, with Steinbrenner indicating the team would discuss an offer with Judge before Opening Day.

“I was happy that when we talked [Tuesday] a little on the phone, they brought up the idea of talking about an extension here soon,’’ Judge said. “I’m focused on doing my work here. Let’s get this arbitration stuff done and then move on to an extension.”

Judge also made it clear he’s involved in the discussions, getting information throughout the day on Tuesday from his agent, Page Odle.

If they don’t match up before Opening Day, the odds of Judge hitting the open market for the first time become significantly greater.

Asked if he would look forward to that opportunity, Judge said: “If it comes to it, maybe. Like I’ve said before, I want to play here. I want to finish my career here. There’s no better place to play. I’m hoping we don’t get to that, but if we do, I think I’ll be ready for it.”

Manager Aaron Boone doesn’t anticipate being a problem, even if there is a hearing during the season.

“The bottom line is there is a business side to this sport and we all understand and respect and navigate our way through it,’’ Boone said. “If it comes to it, we’ll have those conversations, but Aaron is not only a great player but a pro.”