Aaron Boone has one thing at the top of his wish list this holiday season: Yoshinobu Yamamoto.

Boone was part of the Yankees’ contingent that met with the Japanese right-hander twice in hopes of getting the biggest free agent still on the market to come to The Bronx.

“It’s been fun to get to meet him a couple times and be around him and have conversations,’’ Boone said. “Now we’ll see how it goes. I know all teams are now putting their best foot forward and negotiating. That’s above my pay grade. We’ll see where he lands.”

In an effort to get him to the Yankees, the team met with Yamamoto in Los Angeles with his agent, Joel Wolfe, as well as in Manhattan.

Boone added they gave him a Yankees jersey with No. 18, the number he’s worn with the Orix Buffaloes: “It’s his if he wants to keep it.”

Though the Yankees didn’t bring along any of their former Japanese stars, Boone said they did include Hideki Matsui in their pitch, with a video.

Boone said Yamamoto was “aware of a lot” of the Yankees’ history of success with Japanese players — including Matsui, Masahiro Tanaka and Ichiro Suzuki.

“Hopefully those are things that matter to him,’’ Boone said.

The meetings, which also included general manager Brian Cashman and pitching coach Matt Blake, afforded both sides a chance to get to know each other better, and Boone was impressed by what he learned about Yamamoto.

“I think he wants to be great,” Boone said. “I think that’s what’s important to him. I think he’s been looking forward to this.”

The Post’s Jon Heyman reported Thursday the Yankees have made a “significant bid” for Yamamoto but have yet to hear his decision. The Mets are among the other teams bidding for his services, and SNY reported Thursday they had submitted “a very substantial offer.” Meanwhile, the Giants have been told they’re out of the bidding for Yamamoto, according to NBC Sports Bay Area, with expectations he will choose the Dodgers, Yankees or Mets.

The 25-year-old has won the equivalent of the Cy Young award in Japan each of the previous three seasons, and he’s expected to get a contract that could approach — or even exceed — $300 million.

That’s territory not many pitchers have touched, but Gerrit Cole is among them, and Boone added he saw some aspects of Yamamoto’s approach to the game that reminded him of his current ace.

“There are some similarities between him and Gerrit, in how dedicated and disciplined and all-in they are on pitching and baseball and their body and how to be successful,’’ Boone said. “Different personalities.”

Boone said they also talked about the team’s history and biggest rivalries.

“You could see those kinds of competition things kind of light him up a little bit,’’ said Boone, who teamed with the 44th Precinct and the Food Bank for New York City at a food and toy distribution pop-up in The Bronx on Thursday.

The Yankees would pursue Yamamoto regardless of their pitching needs, since they believe he’s a unique talent, but whether they sign him or not, they likely need more pitching — in part due to the trades they made this offseason to land Juan Soto and Alex Verdugo.

“The Soto deal took a while because we were trying different iterations to keep certain people out of it,’’ Boone said of the trade that sent Michael King, Jhony Brito and Randy Vasquez, as well as right-handed pitching prospect Drew Thorpe, to San Diego. “In the end, it’s Juan Soto. It’s gonna hurt.”

But the manager added, “We do feel good about the next crop [of young pitchers]. Whether it’s [Will] Warren, Luis Gil coming back [from Tommy John surgery] or [Chase] Hampton, there are a lot of guys pushing up to the next level.”