Paul, who has sat out 16 games because of a separated right shoulder, has been doing some shooting and running drills on his own. He hasn't practiced with the team because the Clippers haven't practiced recently.
But after the Clippers had a shootaround Monday, Coach Doc Rivers said Paul "gets on the floor and we go over plays."
Paul was injured Jan. 3 at Dallas. If he were to come back Friday, Paul would have been sidelined for five weeks.
"He hasn't had any contact," Rivers said. "But I would say hopefully by the end of the week, I'm assuming he will be. I doubt if we practice. That's the problem… But we can always do three-on-three stuff."
But Rivers said it wasn't necessary for Paul to get in a practice before he plays in a game.
"I think he's pretty good," Rivers said, laughing.
Vujacic returns to L.A.
"It's been different," he said. "It's been tough. That's in the past and I'm ready to keep moving forward."
Vujacic played six-plus seasons with the Lakers, winning NBA championships with them in 2009 and 2010.
"He's another shooter," Rivers said. "We'll see what he's got. He could help us."
"They are going to need a lot more mirrors in the locker room. Hair clips," Shaw said with a laugh. "I don't know if he still wears his hair real long. No, Sasha as a guard, he has the ability to play the one [point guard] and the two [shooting guard]. He can shoot the ball very well from the outside."
Shaw also said he voted for Clippers center DeAndre Jordan to be a reserve on the Western Conference All-Star team. Jordan wasn't selected.