"I don't think it will be too far off," Francona said, "Because he's been doing everything."
Perez has been on the 60-day disabled list with a fractured right thumb since May 1. The injury occurred when he made a diving tag on Odubel Herrera at home plate in the fifth inning of a 4-3 loss to the Phillies on April 30.
The Tribe's backup catcher ultimately underwent surgery on May 6 and was expected to miss eight to 12 weeks.
Before his injury, Perez had played in just four games and hadn't recorded a hit in eight at-bats. A season ago, he batted .228 with seven home runs and 21 RBIs in 70 games.
With Perez on the DL, the Indians acquired Chris Gimenez from the Rangers on May 4 for cash. In his third stint with Cleveland, the 33-year-old had batted .219 (14-for-64) with two home runs and four RBIs entering play Wednesday.
Gimenez's primary contribution has come behind the plate, where he's served as Trevor Bauer's batterymate. In 11 games with Gimenez as his catcher, Bauer has posted a 2.80 ERA and a 65:23 strikeout-to-walk ratio across 74 innings.
Pat James is a reporter for MLB.com based in Atlanta and covered the Indians on Wednesday. This story was not subject to the approval of Major League Baseball or its clubs.