Mauer went 0-for-3 and caught seven innings Saturday night in his second rehabilitation game with Class-A Fort Myers. He was 2-for-4 with two RBIs and caught seven innings Friday night.
Mauer is scheduled to DH on Sunday and then catch nine innings for Fort Myers on Monday. A decision will then be made then on when he'll return to the Twins.
"He feels really great right now," said Minnesota manager Ron Gardenhire, who spoke with Mauer on Saturday.
Mauer hasn't played for the Twins this season and Gardenhire doesn't want to rush him. The original plan called for Mauer to rejoin the Twins on May 1, but the two-time All-Star wants to push that timetable up.
"He told me to keep an open mind," Gardenhire said with a laugh.
"He is unique," Gardenhire added. "He needs fewer at-bats to get back than most people. The at-bats are not an issue. Catching is an issue. It's not just his back. It's his back, his knees and his hamstrings. We want to make sure everything is ready."
The Twins complete a three-game series in Cleveland on Sunday and open a series at home Monday against defending American League champion Tampa Bay.