Leonard, who injured his left ankle Tuesday, could have played in Thursday night's semifinals-clinching 114-75 win over the Houston Rockets if needed, but the Spurs decided they'd rather have him healthy for Sunday, the source said.
Leonard received treatment on his ankle throughout the day Thursday and spent the game in the Spurs' locker room and not on the bench. Coach Gregg Popovich announced before the game that Leonard wouldn't play, adding that it wasn't the player's decision to sit.
Jonathon Simmons started in Leonard's place against the Rockets on Thursday night and scored 18 points.
By sitting out, Leonard, who is averaging 27.8 points on 52.4 percent shooting during the playoffs, now has more time to heal before the Western Conference finals. Before Thursday, the Rockets had been 17-5 at home when facing elimination over the past 25 postseasons, the best record in the NBA in that span.
According to ESPN Stats & Information, the Spurs are now 5-0 in games without Leonard and Parker this season.
Leonard sat out much of the fourth quarter of Game 5 on Tuesday and didn't take the court for overtime after he came down on the foot of James Harden while turning to run up the court with 5:37 left in the third quarter.