"Honestly, I don't think he'll play, but we'll find that out," Rivers said when asked about the shooting guard who has been sidelined for two weeks because of a sore right ankle.
"He can play, so I'm not saying he's not, and it would be very nice if he does," Rivers added, "but he's just not moving well and we'll just find out."
Allen, 36, said he would make a game-time decision on playing.
"There's actually no swelling right now," he said. "But there is still pain to deal with."
Allen averaged 14.3 points a game for the Celtics during the regular season.
If he cannot play, Avery Bradley is expected to start in his place.
"There's the one (lineup) with Ray and the one without him," Rivers said. "That's tough for Avery and Mickael (Pietrus), but both of those guys have been able to deal with that all season. That's been great for us."