The Mets have extended offers to star free agent left fielder Jason Bay as well as top catching target Bengie Molina.

Though the Molina offer had been widely anticipated, the Bay proposal is more surprising. The Mets had seemed to prioritize right-handed pitcher John Lackey over Bay and fellow free-agent outfielder Matt Holliday.

According to a Mets source, the initial four-year offer to Bay is for more than $60 but less than $65 million. Bay has already rejected a four-year $60 million deal made by the Red Sox.

The offer to Bay accentuates the Mets’ growing exasperation with the surprisingly high prices for middle-tier free agents. The Mets have now begun to reason they might as well spend more to get one of the few star-level talents on the market.

Bay, 31, hit .267 with 36 homers and 119 RBIs last year for Boston. He had a .384 on-base percentage and stole 13 bases. However, there is real concern about his defense, especially if he is not regularly protected by the Green Monster.

The Mets once had Bay, but in an ill-fated deal traded him to the Padres seven years ago for Jason Middlebrook and Steve Reed.