Paul, who is out because of a separated right shoulder, did some work at the Clippers' shoot-around Wednesday, playing in a few one-on-one sessions.
Instead, Rivers indicated Paul probably would return when the Clippers play the Philadelphia 76ers on Sunday at home.
"He did some one on ones today and looked pretty good," Rivers said. "So I think he's very close. I don't want to give a day or anything.
"I don't think he'll play Friday, but he could play after that. But I don't know that."
Paul has sat out 17 games because of the injury.
When he was first injured Jan. 3 at Dallas, the Clippers said Paul would be out up to six weeks.
That timetable would have put Paul out until sometime next week.
But Paul has been doing some drills and shooting the last few weeks, making it look as if he could return sooner.
But Rivers said Paul hasn't done enough contact in a five-on-five practice yet.
"Today in one on ones, he took contact," Rivers said. "But it's still not a five on five. We may go [practice] tomorrow [Thursday] or Saturday just to get him some contact."
When Paul does return, Jared Dudley said there will be an adjustment period.
Dudley said Blake Griffin has become more of a focal point for the team with Paul out.
Dudley said they'll have to figure out a way to go through Griffin and Paul.
"You've got to be able to throw it down to Blake sometimes and yet let CP do his thing," Dudley said. "That's going to be the next adjustment period when he comes back. I think in the first couple of games, we'll still be feeding Blake the ball a lot."
J.J. Redick is sidelined
Clippers guard J.J. Redick didn't play against the Miami Heat on Wednesday night because of a sore right hip.
Rivers said Redick was dealing with hip and back issues during Wednesday morning's shoot-around.
"I pulled him out of shoot-around today," Rivers said. "He just didn't look like he could go."
Jamal Crawford started in place of Redick.
The 6-foot-4 Redick has been dealing with injuries all season.
Redick sat out 21 games because of a broken right hand and torn ligaments in his right wrist. He has played with a bruised left knee, a sore right shoulder and back spasms.
Redick is averaging 15.7 points and 28.8 minutes per game.
He is shooting 45.9% from the field, 39.6% from three-point range.