Anthony, who traveled with the team to California, has missed the past three games with a sore and stiff right knee, which he injured March 4 in Cleveland.
An MRI taken recently revealed no structural damage in the knee, but there was some fluid buildup in the back of it.
"I know he's getting his treatment and you don't always have to drain," Knicks coach Mike Woodson said Saturday. "You can treat and the swelling can go away that way as well. We've just got to give it time and see what happens."
If Melo can't go Monday night, Woodson plans to give more minutes to forward Chris Copeland for extra offense. The 28-year-old rookie scored 12 points in only seven fourth-quarter minutes on Saturday night in a win over the Jazz.
"Cope can score the basketball," Woodson said. "On our bench, I need guys that can score. I'm not going to hesitate to throw Cope in because I know he can do that. ... [On Saturday night], I thought he proved a little bit that he deserves to be on the floor."
You can follow Jared Zwerling on Twitter.