Rivers added that Paul fully participated in Wednesday's shootaround prior to the Clippers' 115-106 win over the Memphis Grizzlies.
Paul has missed seven of the Clippers' past eight games with a strained left hamstring, including Wednesday's contest.
"Chris looked great today, had a full workout, played up and down," Rivers said before the game. "He looked terrific. We'll wait to see how he feels tomorrow. Obviously, again, if it was a playoff game, Chris would be playing. But we just want to make sure he doesn't have any soreness.
"If he doesn't, then he's cleared."
The Clippers have won back-to-back games after previously dropping six in a row.
Despite Rivers' assurances, Paul is taking his recovery day-by-day.
"I don't know. I just keep saying, 'Big picture,'" Paul said before Wednesday's game. "But the minute I feel like I can play, I'm going to play."
Paul is averaging 17.7 points, 9.5 assists and 5.3 rebounds this season.
The Clippers are still without Blake Griffin until later this month. The big man has been out since undergoing right-knee surgery on Dec. 20.
Rookie Brice Johnson, the team's first-round draft pick, participated in limited drills on Wednesday. Johnson has been out since the preseason with a lower back injury.