Griffin ended a streak of 197 games played when he sat out Monday's loss to the Washington Wizards with the left hamstring injury and did not go through shootaround Wednesday morning. He will be re-evaluated Thursday before the Clippers play the Miami Heat on Friday.
Crawford has been ruled out of Wednesday's game with a sore right shoulder. He suffered the injury against the Toronto Raptors last Friday and is "day to day," according to the team.
This will be the ninth straight game and 12th overall Paul has missed this season with a bruised right kneecap.
The five-time All-Star injured his knee with 54 seconds left in the Clippers' 104-101 loss to the Magic on Jan. 12 when he collided with Orlando guard J.J. Redick.
Clippers guard Eric Bledsoe has started the 11 games Paul has missed, with the team going 5-6 during that time.
Billups has been out with peroneal tendinitis in his left foot and has played only three games this season. Although Billups didn't go through shootaround on Wednesday, he believes Thursday's practice will let him know whether he can come back before the end of the Clippers' road trip.
"I'm looking forward to practicing tomorrow and going up and down," Billups said Wednesday. "Tomorrow I'll be able to compete and see how I feel."