Reyes, who has been on the 15-day disabled list with a right shoulder impingement, threw 12 pitches during a one-inning stint for Class A Vero Beach on Monday. He was eligible to come off the disabled list on Thursday.
"Al Reyes threw well in Vero but still feels as though he needs one more time out," Rays manager Joe Maddon said. "We're going to give that to him on Thursday. He's going to pitch in [an extended Spring Training game] on Thursday, again, just to fulfill his own feeling about how he feels. So we respect that, and that was fine."
Reyes led the team in saves in 2007 with 26, but was moved to a setup role this season to accommodate the addition of closer Troy Percival. Reyes is 1-2 with a 9.00 ERA in seven appearances this season.
"I really believe it's just going to be one more [rehab appearance before Reyes is ready]," Maddon said. "He felt better about the other day than he did the first time. And again, he wants to know in his mind that he can go two days in a row. So in his mind he just needed to pitch one more time to insure that he will pitch well when he gets back."
The Rays will re-evaluate Reyes' situation on Friday after seeing how Reyes feels the day after the outing.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.