Carlos Correa landed a Giant new contract Tuesday night that followed a flirtation by the Mets.

The All-Star shortstop agreed to a 13-year deal worth $350 million with the Giants, a source confirmed to The Post’s Jon Heyman, ending the Mets’ late inquiry into potentially pairing the 28-year-old Correa with Francisco Lindor on the left side of the infield. Correa presumably would have shifted to third base.

A club source, when asked specifically about Correa hours before his agreement with the Giants, described Mets officials as trying to remain “opportunistic” on the free-agent market as they look to improve the team.

Correa spent last season with the Twins — he opted out of his contract in November — and posted a .291/.366/.467 slash line with 22 homers and 64 RBIs in 136 games. The Giants were evidently hungry for a big splash after missing on Aaron Judge, who last week returned to the Yankees on a nine-year contract worth $360 million. The Giants also extended an offer to Brandon Nimmo before he returned to the Mets on an eight-year contract worth $162 million.

The Mets’ payroll for next season already stands in the $345 million neighborhood following contracts for Justin Verlander, Nimmo, Kodai Senga, Jose Quintana and David Robertson that were agreed to in the last 1 ½ weeks. Including penalties as a team above the top tier of the competitive balance tax, roughly $421 million is committed to payroll for next season.

Correa is the latest shortstop to command a mega-deal. Two others, Trea Turner and Xander Bogaerts, received 11-year contracts worth $300 million and $280 million, respectively. Turner signed with the Phillies and Bogaerts with the Padres.

The Twins offered Correa a 10-year contract worth $285 million, according to Heyman. The Cubs were another team linked to Correa.

If the Mets had signed Correa, they would have likely traded Eduardo Escobar — who is under contract through next season — and decided on how to proceed with rookie third baseman Brett Baty.

Last season the Mets finished fifth in MLB in scoring, but their lineup appeared overmatched in getting swept three games by the Braves that ultimately decided the NL East race. The Mets were similarly quiet offensively in losing the best-of-three wild-card series to the Padres.

At the very least, the Mets are still searching for another outfielder who can augment Nimmo, Starling Marte and Mark Canha.

Team owner Steve Cohen has already approved $465 million in contracts this offseason.