Neither played Thursday night against the Utah Jazz at EnergySolutions Arena, meaning they have missed a combined 24 games this season.
Leonard, the second-year player from San Diego State, has been sidelined for 13 games because of knee tendinitis.
Jackson, meanwhile, has missed the past 11 games because of a fractured finger.
Both players were in Utah with their teammates, but neither returned to the lineup against the Jazz.
"Kawhi went through the [morning] shootaround," coach Gregg Popovich said. "... Maybe he gets some minutes in the next one, two [or] three games. We'll see how he feels. But he's getting real close."
According to Jackson, he's also on the threshold of returning.
"I feel like I'm ready to play, but coach wants to hold me out a couple more games," Jackson said. "My thing is, I just want to get in a couple of practices so I can get hit on the finger and see how it reacts."
Jackson knows conditioning might be an issue at least for a while.
"... I really feel like I'm ready to go," he said. "[But] playing is the only way you can get in shape. I know that."
Because of the injury to Leonard, Popovich was forced to juggle his starting lineup.
He switched Danny Green from shooting guard to small forward and replaced him in the backcourt with Gary Neal, who is averaging 12.3 points per game.
"Gary ... has been an important part of our team," Popovich said. "His defense gets better and better. He shoots the ball. He's a heck of a weapon offensively, as far as his shot is concerned. He really spreads the floor for us. So he's been real important."
Neal has been so impressive that Leonard might have a difficult time reclaiming his role as a starter.
"As [Neal's] defense gets better," Popovich said, "it makes it tough for me to decide who I want on the floor. And that's a player's job: make it tough on the coach."