The 38-year-old's contract will pay him $700,000 if he's in the Majors and $90,000 if he's in the Minors, according to the report. He can also earn $150,000 in bonuses as he gets $30,000 each for 20, 30, 40, 50 and 60 relief appearances.
The 13-year veteran made 28 relief appearances with the Mets last season, posting a 3.31 ERA with 14 strikeouts in 32 2/3 innings.
In his career, Dessens is 48-62 with a 4.53 ERA while playing with the Pirates, Reds, D-backs, Dodgers, Royals, Brewers, Rockies, Braves and Mets.
Rhett Bollinger is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.