Percival, who has been on the disabled list with a left hamstring strain since May 29, is the team's closer, and he is 14-for-16 in save opportunities this season.
Percival said his leg "definitely feels stronger than it has."
"I'm sure [some discomfort is] still going to be there, but it definitely feels stronger and I don't think I'm going to have any more problems with it," Percival said.
Percival has worked with the Rays' training staff to employ exercises for isolating and strengthening the problem area. The veteran right-hander threw a simulated game Tuesday in Anaheim.
"I felt real good during my sim[ulated] game the other day," Percival said. "It took about 10-12 pitches before I had full confidence in it, before I was letting it go, then it was fine."
Rays manager Joe Maddon said that Percival will be used as he had been before going on the DL.
"We're not going to change anything," Maddon said. "[Percival will be used] a couple of nights in a row, maybe three nights if he hasn't thrown too many pitches; I don't have a problem with that. As of this moment, I don't have any plans of alternating that."
Reyes is beginning his second stint on the DL this season, as he was shelved from April 16-May 13 with a right shoulder impingement.
"I'm just going to keep going to training room and hope it gets better," Reyes said.
Given the way the Rays have performed this season, Reyes wants to be able to contribute down the stretch.
"I just want to be ready for that," Reyes said.
Maddon said Reyes told him he felt fine when he first came off the DL, but "it just didn't want to come around."
"It's incumbent on us to get him well," Maddon said. "Let's move it along, and that's what we're going to do. ... It's one of those things that needs to be calmed down."