The All-Star starter, out since late last month with a sore left elbow, was scheduled to pitch in a minor league game Thursday before rejoining the rotation Sept. 3 on the road against the Los Angeles Angels, manager Joe Maddon said.
Moore was 14-3 with a 3.41 ERA before Tampa Bay put him on the disabled list July 31 for what was hoped would be a two- or three-week stay.
The Rays (74-54) stand one game back in the division behind the Red Sox after a loss Sunday to the Yankees.
Moore threw 49 pitches Saturday in a simulated game.
He said Sunday, according to the Tampa Tribune, that he had felt the normal soreness he would after pitching in a regular game and would try to talk Maddon into letting him return this week.
"Whatever gets me back in the rotation," he said, according to the Tampa newspaper. "That's the ultimate goal."