Smart had surgery to repair a torn ulnar collateral ligament in his right thumb on March 16 with an estimated recovery time of six to eight weeks.
The injury occurred during a March 11 game against the Indiana Pacers when he dove to the ground for a loose ball.
Stevens told reporters on a conference call Saturday that Smart was getting closer to being cleared for live game action.
"I think it's just a matter of you have to have that post-surgery healed to be able to take a hit even with the brace on it," he said. "That's the hold-up. Other than that, I think he feels pretty good. He's shooting the ball, he's doing everything in a workout that you can do. It's just a matter of being cleared for live play."
Smart's return will ease the burden on Terry Rozier, who is averaging 36.3 minutes per game against the Bucks.
The Bucks and Celtics are tied at two games apiece heading into Tuesday's matchup at the TD Garden.