Durant has been out injuring his calf May 8 in a victory over the Houston Rockets in the Western Conference Semifinals. The former NBA MVP was averaging 34.2 points, 5.2 rebounds, and 4.9 assists in 11 playoff games before his injury.
"He's doing more today," Kerr told reporters. "We'll know more after that."
Kerr said Durant will do extra work with the team's younger players before the Warriors "gauge" his progress.
Kerr said before the Warriors' Game 4 loss that Durant had not suffered a setback in his recovery.
The Warriors need to win three straight games to avoid losing their first NBA Finals since 2016. The Toronto Raptors took a 3-1 series lead with Friday's 105-92 in Oakland, Calif.
Game 5 will be played at Scotiabank Arena in Toronto on Monday night.