Price has been sidelined by a strained left triceps since May 15. The left-hander was placed on the disabled list for the first time in his career on the following day.
Rays manager Joe Maddon said last Friday that the team felt "pretty strongly" that Price would be ready to rejoin Tampa Bay's rotation this week.
The Rays have not announced a corresponding roster move.
The American League's reigning Cy Young Award winner, Price had gotten off to a slow start this season prior to the injury, going 1-4 with a 5.24 ERA in nine starts.