Billups has missed the past four games with a bruised left thigh. The Knicks are 3-1 without the 34-year-old veteran.
"It could be another day or so but we're still hoping that [Wednesday] he wakes up feeling pretty good," D'Antoni said after practice on Tuesday.
Billups suffered the injury last Tuesday against Orlando when he collided with Magic center Dwight Howard.
The Knicks hoped to have Billups back for Monday's 131-109 home win over the Utah Jazz but he was ruled out prior to tip-off due to the lingering soreness in his thigh.
Billups has had difficulty pushing off and stopping with his left leg.
Instead of participating in practice Tuesday, Billups opted to receive treatment. He was not available to the media.
Backup Toney Douglas filled in for Billups and the Knicks didn't miss a beat against the Jazz, outscoring them 40-24 in a first quarter in which Douglas had 12 points and two assists. He finished with 20 points on 6-of-9 shooting and hit 5-of-7 from beyond the arc. Douglas has averaged 16.3 points, 5.8 assists and two turnovers in four starts in place of Billups.
"You don't ever want to lose your point guard ... but at the same time, Toney's had two great games so his confidence and ability to run the team when Chauncey won't be in there I think has gone up," D'Antoni said Tuesday.
Big man Ronny Turiaf missed Monday's game -- his third straight -- with a sore left knee and was replaced by Jared Jeffries. Jeffries finished with six rebounds, three assists and several hustle plays on loose balls in 23 minutes.
Turiaf is also questionable for the Memphis game.
Jeffries is expected to remain the team starter after Turiaf's return.
Bill Walker also missed his second straight game with a sore left knee on Monday. Walker predicted that he would be back for Wednesday's game in Memphis. He is listed as probable for the game.
Both Turiaf and Walker participated in practice Tuesday and D'Antoni seemed optimistic that they would suit up against Memphis. But he was less confident about Billups.
"They're all upgraded a little bit ... I think Chauncey's maybe the furthest away," the coach said.
Billups has been a linchpin for the Knicks (33-29), averaging 23.3 points and six assists in four games with New York. Billups was acquired in the three-team, 13-player deal that brought Carmelo Anthony to New York on Feb. 22.
The Knicks have added seven new players since the Anthony trade and Billups' absence has hindered the team's ability to develop defensive consistency.
"Once Chauncey gets back we can really figure out our chemistry on both ends of the court," Amare Stoudemire said.
The Knicks are in sixth place in the Eastern Conference, just a game ahead of the Philadelphia 76ers and 3½ games behind the Hawks for fifth. They are 5-3 since acquiring Anthony and Billups.
The Knicks hit the road for back-to-back games against Memphis, which beat Oklahoma City on Monday and has won eight of its past 11, and Dallas, which owns the third-best record in the NBA (46-17).
Ian Begley is a regular contributor to ESPNNewYork.com.