Perez was diagnosed Friday with a strained muscle in his right shoulder, an injury that could sideline him for a month.
"The way it feels, just moving around, it gets better every day," Perez said Saturday.
Perez pitched an inning Tuesday during a 4-1 loss to Kansas City and felt pain in the shoulder Thursday. The right-hander said the injury is not as serious as the strain he suffered last spring to a muscle on his left side in his first bullpen session on Feb 23.
He made it back for the opener, when he allowed three runs in the ninth against Toronto in a game the Blue Jays won in 16 innings.
"I was more concerned last year," said Perez, a 2011 and 2012 All-Star who saved 39 games in 43 chances last season. "I think that if this was regular season, I could have managed it. But this is spring training. It's early. We're playing this a lot slower than we would if it was July and we were in the middle of the race."
Indians manager Terry Francona didn't want to set a timetable for Perez's return.
"Is it on opening day? We'll see," Francona said. "If he's a week late, he's a week late. That's the way it goes."
Perez, who has 98 saves during the last three seasons, is frustrated he had to withdraw from the U.S. team headed to the World Baseball Classic.
"The WBC is important. To this point, it's the biggest honor in my career," he said. "Yeah, it's disappointing, but it would have been a lot worse if I had pitched and then been out for three or four months."