Boesch came out of Wednesday's game in Cleveland after aggravating his sprained right thumb and did not play in the Tigers' weekend series in Baltimore until he pinch-hit in Sunday's 8-5 defeat.
Leyland said Boesch would hit off the tee before Sunday's finale, and if he does well in batting practice Monday, he could make it back for Tuesday's game with the Twins.
"He'll play if he's OK," Leyland said. "But I can't swear to that either. He's always ready to go, which I really admire about him. I love him. He's a tough kid."