Marmol was once considered one of the best relief pitchers in the league but has struggled in recent years.
After spending more than seven seasons with the Chicago Cubs, Marmol had short stints with the Los Angeles Dodgers and Miami Marlins, who released him in May after he posted an 8.10 ERA over 15 appearances with the team.
Marmol later signed with the Cincinnati Reds, but the team released him in November after he recorded a 7.36 ERA in three games with Triple A Louisville. Marmol, 31, reportedly has been pitching with a "new arm slot."
Cleveland currently ranks 16th in MLB in bullpen ERA.