Mets LHP Jerry Blevins, RHPs Bartolo Colon and Fernando Salas, 1B James Loney, infielders Kelly Johnson and Neil Walker, and OF Alejandro De Aza filed for free agency on Thursday.
The Mets would like to retain Blevins, 33, but expect him to receive a multiyear offer elsewhere, Adam Rubin of ESPN reported Wednesday.
The 43-year-old Colon and the Mets have interest in reuniting, though Colon might be looking for a two-year deal.
It's expected that the Mets will extend the $17.2 million qualifying offer to Walker. If he rejects it and signs elsewhere, they would receive a compensatory draft pick.
Monday is the first day that free agents are allowed to negotiate with other teams.