The 32-year-old is coming off rotator cuff surgery and must pass a physical before spring training, the newspaper said.
Garland went 1-5 with a 4.33 earned run average in nine starts in his injury-interrupted 2011 season.
He could provide some insurance for the Indians, who are dealing with the uncertain legal status of Fausto Carmona, whose real name is Roberto Hernandez Heredia. Carmona/Heredia has visa issues in his native Dominican Republic after being arrested last month for double identity.
Garland spent eight seasons with the Chicago White Sox, where he had an all-star season in 2005 when the club won the World Series.
He later pitched for the Los Angeles Angels, Arizona, the Los Angeles Dodgers and San Diego.
For his career, Garland is 132-119 with a 4.32 ERA in 330 starts.