Maine spent five of his seven seasons with the Mets; his last stint was in 2010.
In 108 career games, the 6-foot-4 right-hander is 41-36 with a 4.35 ERA.
His best season was in 2007, when we went 15-10 with a 3.91 ERA in 32 starts for New York.
A sixth-round pick of the Orioles in 2002, Maine pitched in parts of two seasons with Baltimore (2004-05).
In 2012 he went 8-5 with a 4.97 ERA in 16 games (15 starts) for Triple-A Scranton/Wilkes-Barre (Yankees).
Miami has been looking for starting pitching with previous big league experience.