Manager Ron Roenicke was heartened by Braun's response to a batting cage session Tuesday. Braun was scheduled to take some more swings and play some catch before Wednesday's game against the Washington Nationals.
Braun has been out since June with a bruised right thumb, and the Brewers lineup has suffered mightily without the 2011 NL Most Valuable Player.
Roenicke said Braun might be able to return before the All-Star break, which would be earlier than previously expected.
"With the progress that he made the last couple of days, I think it's a possibility," the manager said.
Braun said Tuesday night that the thumb is not "pain-free" but is "a lot better than it was."
Meanwhile, Peralta was able to work out in the weight room and play some catch a day after a strained left hamstring forced him from a game in the sixth inning.
Nevertheless, Peralta's next scheduled start, on Sunday against the New York Mets, is in jeopardy and likely will be determined by the training staff.
"I think that's still iffy. ... To put him back out there if they don't think he's 100 percent, I don't think we'll do that," Roenicke said.