"Klay will warm up and we'll see," Kerr said. "But he was doing better this morning when he checked in with the training staff, so I'm hopeful that he will play."
Kerr also ruled Andre Iguodala (left lateral leg contusion) out for Game 2, but is "optimistic" he will play at some point during the series.
"He has gotten better gradually, but there's no way of knowing for sure at this point," Kerr said.
Thompson was listed as questionable entering Sunday's game with what a source told ESPN's Ramona Shelburne was a high left ankle sprain. He sustained the injury in Golden State's Game 1 win, when Cavaliers guard JR Smith inadvertently undercut his left leg while trying to pick off a pass. Thompson briefly exited the game to receive treatment in the locker room but returned soon after.
Thompson did very little at practice Saturday and was seen walking around Oracle Arena gingerly, with a noticeable limp.
Nevertheless, the 6-foot-7 sharpshooter said he was "planning on playing" in Game 2 and was doing "everything I can to minimize the swelling."
ESPN's Chris Haynes contributed to this report.