"You know, as we looked at ways to improve the roster and improve the bench, versatility is one thing we wanted to maintain," said Red Sox manager John Farrell. "Michael obviously gives you that with the ability to play three infield positions. He can run, he is a switch-hitter who is better from the left side of the plate."
The Red Sox hope Martinez will arrive by Saturday.
Martinez was designated for assignment by Cleveland last Saturday after hitting .283 with three doubles and one home run in 32 games for the Indians this season.
The versatile 33-year-old is a .199 career hitter with the Phillies (2011-13), Pirates (2014) and Indians (2015-16).