Hal Steinbrenner ‘willing to consider’ any Yankees improvements as Blake Snell looms

TAMPA — The Yankees are already at a record payroll and above the highest luxury-tax threshold, but Hal Steinbrenner indicated he is not closing his checkbook just yet.

Steinbrenner on Thursday said the Yankees “have a championship-caliber team right now,” but added that they “haven’t stopped looking to improve, and we never will.”

Though he declined to address free agents like Blake Snell, the Yankees’ managing general partner said a team can never have enough pitching.

“I’m just going to tell you that we continue to look at a lot of different options,” Steinbrenner said after the Yankees’ third full-squad workout of spring training. “Given where we are payroll-wise, any addition to the club is going to be a costly one, but I’m still willing to consider anything that comes my way, anything [GM Brian Cashman] and his team brings my way. I’ll leave it at that.

“But we are not done trying to improve this team.”

As currently constructed, the Yankees’ projected luxury-tax payroll stands at around $306.7 million, per Cot’s Contracts.

Any dollar the Yankees spend beyond the highest luxury-tax threshold of $297 million will come with a 110 percent tax, making additional moves even pricier.

“There’s still things we’re looking at, whether it’s trades or signings,” Steinbrenner said. “I’m not saying anything is going to happen, I’m not saying something’s not going to happen. But I’m still willing to improve this team however we can.”

There is plenty of motivation to do so, coming off a brutal 82-80 season.

Steinbrenner echoed captain Aaron Judge by saying he was “embarrassed” by the Yankees’ worst season in 30 years.

“I don’t think there’s one person in this organization that wasn’t embarrassed,” he said. “I think we have something to prove to fans after last year, absolutely. No doubt.”

There is also pressure on the Yankees to go all-in this season after giving up a package of players to land superstar Juan Soto in December, one year before he hits free agency.

Steinbrenner said he hoped it would not just be a one-year partnership and indicated he would be open to considering an extension before the season started, though Soto is widely expected to test free agency.

Still, Judge recently said he hoped the Yankees might have another move in them.

“He and I talk about it, but he also understands where I sit and the decisions that I have to make and the reasons I have to make or not make those decisions,” Steinbrenner said.

While pitchers like Snell and Jordan Montgomery remain available on the free-agent market with spring training underway, Steinbrenner said there were not any potential moves that he would classify as “close.”

As for trade talks to add another starter (Corbin Burnes has already been dealt to the Orioles while Dylan Cease looms as another target), Steinbrenner said he “wasn’t willing to part with” Will Warren and Chase Hampton, noting the pitching depth the Yankees had already sacrificed in the Soto deal.

He also later mentioned Spencer Jones as someone he would be hesitant to give up in a trade.

“The depth is somewhat concerning to me, but the rotation as it stands is a very good one,” Steinbrenner said.

Steinbrenner made multiple references to the Yankees having up until the trade deadline to add to their roster, pledging to “keep exploring possibilities” before then.

The Yankees had tried to sign Japanese right-hander Yoshinobu Yamamoto during the offseason to bolster their rotation but lost out to the Dodgers.

Then after making an offer to Snell, per The Post’s Jon Heyman, they pivoted to sign Marcus Stroman to a two-year, $37 million deal to fill out their rotation besides Gerrit Cole, Carlos Rodon, Nestor Cortes and Clarke Schmidt.

Steinbrenner said the Yankees were “disappointed” not to sign Yamamoto, but defended their 10-year, $300 million offer.

Yamamoto ended up signing with the Dodgers for 12 years and $325 million.

“I probably went higher than some of our baseball people would have gone,” Steinbrenner said. “But I felt it was important to the fan base and to our chances this year to really make a run and try to get him. I just felt, right or wrong, that the bidding was going to continue and $300 million was a very good offer, and I think a lot of our fans agreed with it.”