The deal is pending a physical and could be official as soon as Wednesday, the sources said.
May, 31, was 1-0 with a 3.86 ERA and two saves in 24 appearances for the Minnesota Twins last season.
His velocity has consistently risen, from 91.9 mph in 2014 to 96.4 mph in 2020, with a full-time switch to the bullpen in 2016 and Tommy John surgery in 2017.
May has spent all six seasons in the majors with the Twins and is 23-21 with a 4.44 ERA and seven saves in 215 appearances, including 26 starts.
New York’s front office is being run by Sandy Alderson, who returned to the Mets as team president on the day that Steven Cohen completed his $2.42 billion purchase from the Wilpon and Katz families.
The news of May’s agreement was first reported by SNY.
ESPN’s Jeff Passan, Kiley McDaniel and The Associated Press contributed to this report.
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