MLB.com, which cited a baseball source, reported the deal and said it includes an invitation to spring training.
Durbin, 34, pitched for Cleveland in 2011 and posted a 5.53 ERA in 56 appearances.
In his 12-year career, Durbin has logged a 5.10 ERA and 38-46 record in 364 appearances (75 starts). In addition to the Indians, he has played for Philadelphia, Detroit, Arizona and Kansas City.
Durbin won a World Series ring in 2008 with the Phillies.