"Melo, probably not," coach Mike D'Antoni said Saturday. "And Monday, it's close."
Anthony shot around at practice, but didn't participate in contact drills. D'Antoni said Anthony didn't suffer any setbacks Saturday.
"Just a little twinge here and there," he said. "We're thinking Monday."
The Knicks play host to the New Jersey Nets that night.
D'Antoni told reporters that Davis, who has been recovering from a herniated disk in his back, could play Sunday, even though he hasn't participated in a full practice lately.
"He's been doing 2-on-2 and 5-on-0 (drills) and he looks pretty good," D'Antoni said. "He's close. He can go."
D'Antoni plans to gradually increase Davis' role in the rotation, and is looking at the week after the All-Star break -- when the team will have four straight practices -- to get Davis even more acclimated to the team.
D'Antoni hopes to bring Smith up to speed Sunday.
Smith, Anthony's former Nuggets teammate, arrives in New York on Saturday night and could dress Sunday. He responded to a fan's question on Twitter by saying he would play against the Mavericks, but D'Antoni laughed that off.
"I'll introduce myself before he plays," D'Antoni said, smiling.
Smith would help shore up the Knicks' 3-point shooting woes. They shot 4-for-24 from downtown Friday night in an 89-85 loss to the Hornets, and they're second-worst in 3-point percentage on the season (29.9 percent).
Anthony would give an assist in that category as well, as he shoots well playing alongside point guards such as Jeremy Lin who can create solid spacing on the court. Last season, with Chauncey Billups, Anthony connected on 53 3-pointers (42.4 percent) after the All-Star break.
Anthony has missed six consecutive games since suffering the injury Feb. 6 against the Utah Jazz. The Knicks (15-16) are 5-1 during that span.
Anthony, who is averaging 22.3 points and 6.0 rebounds, was selected by fans to start in the All-Star Game Feb. 26 in Orlando, Fla.
Mavs guard Jason Terry should be available to play Sunday against the Knicks, coach Rick Carlisle said. Terry missed the past two games, Wednesday against Denver with a mild right quadriceps strain, and Friday at the Philadelphia because of personal reasons.
Jared Zwerling is a regular contributor to ESPNNewYork.com.