"His schedule hasn't changed," Acta said on Friday.
The 38-year-old Damon -- officially signed to a Minor League contract by Cleveland on Tuesday -- is currently at the Indians' training complex in Goodyear, Ariz., going through daily workouts in preparation for games. The outfielder will take part in extended Spring Training games before being moved to a Minor League affiliate.
Acta noted that Damon likely would work as a designated hitter in his first game action.
"We just have to make sure that he's physically fit before we throw him out there," Acta said. "I'm probably anticipating that he's probably going to DH to have some at-bats before he jumps out there in the outfield. It's coming -- soon."
When Damon does join the Indians, he likely will get most of his at-bats as a left fielder. The Tribe already has a full-time DH in veteran Travis Hafner. As things currently stand, Cleveland's outfield alignment consists of left fielder Shelley Duncan, center fielder Michael Brantley and right fielder Shin-Soo Choo, with Aaron Cunningham on the bench.
Center fielder Grady Sizemore, who is currently on the 60-day disabled list due to a lower back injury, is slated to resume baseball activities next week. The Indians are not expecting to have Sizemore back in the fold until the first week of June at the earliest.