After going head-to-head for Juan Soto, the Yankees and Mets battled for Roki Sasaki on the very same day.

Both New York clubs visited Los Angeles on Thursday and made their pitches for the young, star Japanese righty, The Post has learned.

Previously, only the Mets were known to have sat Thursday with Sasaki, who pulled off the doubleheader.

Specifics concerning the meetings were unclear, but the Yankees previously had prepped a virtual presentation that helped them secure the in-person meeting.

On Wednesday, GM Brian Cashman said he did not know how many teams had reached this round of the amateur free-agency battle.

The Cubs were expected to meet with Sasaki on Friday, according to a report from 670 The Score.

Sasaki is known to have been a fan of Masahiro Tanaka.

According to his agent, Joel Wolfe, Sasaki has paid attention to MLB clubs’ track record with Japanese players, overall success and history with developing pitching arms.

All should help the Yankees’ case.

Hurting their case could be the market size (Sasaki, who has had poor experiences with Japanese media, may prefer a smaller city), and Japanese players have favored the closer West Coast.

Plus, the powerhouse Dodgers loom as the most likely destination, and the Padres should have a fighting chance in part because of Yu Darvish, who is close with Sasaki.

The Yankees have been overt with their interest in Sasaki, including visits to Japan from top scouts and Cashman himself.

Every team should be interested in a 23-year-old with an electric arm who can be imported for the price of a young utilityman: Because he is not yet 25, Sasaki is being treated as an international amateur who can only ask for the few million dollars in teams’ international bonus pools.

“He’s obviously a tremendous talent,” Cashman said of Sasaki this week. “It’d be nice to have Yankee Stadium be his home, but the decision will be up to him. All we can do is share everything and anything that we can about ourselves and what we provide.”

Sasaki cannot sign until Jan. 15. If he chooses the Yankees, rotation decisions would have to be made for a group that right now includes six capable arms (Gerrit Cole, Max Fried, Carlos Rodon, Luis Gil, Clarke Schmidt and Marcus Stroman).

Typically teams shift to a six-man rotation to accommodate a Japanese pitcher who is accustomed to pitching once a week.

Cashman this week acknowledged he did not know what kind of chance the club stood.

“All I can tell you is I appreciate having the opportunity to connect,” Cashman said. “After that, ultimately, it’s the individual’s choice.”