Damon and Ramirez will become members of the Rays if they pass their physical exams, the report said. Damon would receive 5.25 million, with another $750,000 possible in incentives, and Ramirez has agreed to a $2 million contract.
Damon played last season with Detroit, where he batted .271 with eight homers and 51 RBI. He spent eight years with Boston and played for the New York Yankees from 2006-09.
He has a career batting average of .287 with 215 home runs, 1,047 RBI and 385 steals.
Ramirez started last year with the Los Angeles Dodgers and wound up with the Chicago White Sox. He had the worst year of his career as far as power numbers were concerned, producing just nine homers and driving in 42 runs.
His career batting average is .313. Ramirez has hit 555 home runs to go with 1,830 RBI.