Coach Doc Rivers said he told head athletic trainer Jasen Powell they wanted to be "way more conservative" with Paul's injury "than aggressive on it."
"But if he's not, we're not going to take that chance," Rivers said. "After Sunday, we have two more days off. So it could be two games. We just don't know yet."
The Clippers are off Monday and Tuesday.
Then they start an 11-day trip with a game in Atlanta on Wednesday and the hope Rivers has is for Paul to be healthy for those games.
"We have a bunch of games coming up," Rivers said. "And it's just smarter to rest him."
Paul tested his hamstring by running before the game in front of Powell, but it was apparent he couldn't go.
Rivers was asked whether Paul, who hates to sit out games, fought his coach on trying to play.
"I think Chris knows it's the right thing to do," Rivers said.
Paul injured his hamstring in the third quarter of Wednesday night's game against the New York Knicks at Staples Center.
Paul is second on the team in scoring (19.0), first in assists (12.2) and second in minutes played per game (35.0).
"Obviously there is very few people who see the floor like Chris," Rivers said. "So when you don't have him, you're going to miss things like that. We just have to make it up in other areas."
Crawford is ready for new role
Crawford, the Clippers' sixth man, is the team's instant offense when he comes off the bench.
But with Paul out, Crawford, who has point-guard skills, said he has to "flip mentalities" from being just a scorer to being a distributor as well.
"You have to find balance obviously," Crawford said. "I think they're as different of mentalities as you can have , as far as shooting and setting guys up. Because a shooter's mentality is to be aggressive and attack and point guard is to set the table for everybody else."
Rivers discusses Jason Kidd's fine
Rivers was asked what he thought about Brooklyn Nets Coach Jason Kidd being fined $50,000 by the NBA for intentionally spilling his drink on the court during a game Wednesday night against the Lakers.
"I saw it live, but I didn't realize it was intentional," Rivers said. "Allegedly. Interesting. It's been thought of, let me put it that way."