Odorizzi has reportedly been linked to the Mets, Minnesota Twins, Toronto Blue Jays, and San Francisco Giants.
The 2019 All-Star spent the last three seasons with the Twins. He accepted Minnesota's $17.8-million qualifying offer last winter. He isn't tied to draft-pick compensation this offseason, while Bauer is.
Odorizzi was held to 13 2/3 innings last season due to multiple injuries, including a chest contusion and blister on his pitching hand. He posted a 6.59 ERA in four starts.
The Mets appear poised to be active in free agency under new owner Steve Cohen. The team already signed reliever Trevor May to a two-year, $15.5-million contract.