Bombers set up Yamamoto sit-down

NASHVILLE, Tenn. — The Yankees have their meeting set with Yoshinobu Yamamoto.

The club will get a face-to-face visit with the coveted Japanese right-hander and his representatives on Monday, The Post’s Joel Sherman confirmed Wednesday, as it tries to land the 25-year-old stud.

The Yankees have scouted Yamamoto extensively, including GM Brian Cashman flying to Japan to watch him in September and seeing him throw a no-hitter. Many of Cashman’s top lieutenants have also been overseas to scout Yamamoto, who has three times been named the top pitcher in Nippon Professional Baseball.

Cashman and manager Aaron Boone gave Yamamoto rave reviews Tuesday, and while they are far from the only suitors for the top pitcher on the free-agent market — the Mets are also making a strong push — they seem to believe they have a real shot to land him. Because of the rabid interest, the total price to land Yamamoto (including the posting fee) could be upwards of $300 million, per The Post’s Jon Heyman.

➤ Gerrit Cole has an opt-out in his contract after next season, but if he triggers it, the Yankees can just add an extra year at the end of the deal to keep him in pinstripes through 2029.

“We would anticipate that those things are going to happen,” Scott Boras, Cole’s agent, said on Wednesday.

If they do, it would bring the total value of Cole’s contract to 10 years and $360 million.

➤ The Yankees’ non-roster pitching depth took a hit in Wednesday’s Rule 5 draft, losing three right-handers — including the top two picks — out of the 10 total players selected.

The Athletics drafted Mitch Spence with the first pick before the Royals nabbed Matt Sauer with the second pick. The Rangers later selected Carson Coleman with the 23rd pick.

All three pitchers, whom the Yankees left unprotected by not adding them to their 40-man roster last month, will have to spend all of 2024 on their new team’s major league roster, or else they will be offered back to the Yankees for $50,000.

The Yankees had stockpiled solid upper-level pitching depth, but some of it is on the move this week. Besides the three pitchers lost in the Rule 5 draft, they traded Richard Fitts to the Red Sox as part of a package for Alex Verdugo and Michael King, Drew Thorpe, Randy Vasquez and Jhony Brito to the Padres for Juan Soto in a blockbuster Wednesday.

➤ Boone said Wednesday that DJ LeMahieu is his third baseman.