Apparently even Steve Cohen has limits.

The Mets never made a formal offer to Shohei Ohtani, The Post’s Mike Puma reported Saturday, after it became clear that the contractual numbers would be higher than the team was comfortable with.

As it turned out, those contractual numbers were historic: Ohtani signed with the Dodgers for 10 years and $700 million, which is believed to be the largest pact in sports history.

Lionel Messi previously held the record for total money in one contract with $674 million. Ohtani’s $70 million per season blows away the prior MLB high, the $43.3 million that Cohen bestowed on Max Scherzer and Justin Verlander per season.

The Mets and Yankees did not appear to be heavily involved in the chase for Ohtani, who didn’t seem to be a fit in New York.

A clubhouse source told The Post’s Jon Heyman that Ohtani has said he could not see himself playing in the Big Apple.

Even if the Mets wanted to chase Ohtani, it became evident to their owner that Ohtani likely was not interested.

“The agent never reached out to me personally,” Cohen told The Athletic, “and I think that’s pretty telling.”

Without Ohtani — or any free agent on a multi-year deal — the Mets have been more judicious this offseason as they focus more on building the foundation through young players and their farm system.

An exception might be made for 25-year-old Japanese ace Yoshinobu Yamamoto.

The Yankees made a different kind of splash by trading for Juan Soto this week.