Pestano, 27, went 3-3 with a 2.57 ERA in 70 relief appearances last season while utilizing a solid sinker. He has only slightly more than two years of major league service time -- meaning he is still under control for four years and not yet even eligible for arbitration.
A source indicated the Mets pursued 36-year-old right-hander Joel Peralta, but have found the asking price too high. Peralta signed with Tampa Bay at $3 million per season through 2014, then has a series of team options.
The Mets also have been trying to engage the Kansas City Royals about bullpen pieces, but have not made headway.