After the team's shootaround in Toronto, Anthony told reporters that he will use Thursday as another day to rest and is hopeful to return to the court Friday against the Phoenix Suns.
The Knicks are 0-5 in games Anthony has missed for injury this season.
The 31-year-old initially experienced soreness in his left knee last week and sat out the fourth quarter of Saturday's loss to the Charlotte Hornets. He also missed Tuesday's loss to the Oklahoma City Thunder.
Any soreness in Anthony's left knee is cause for concern; he underwent surgery to repair a patella injury in his left knee in February and missed the remainder of the 2014-15 season.
But both Anthony and Knicks coach Derek Fisher are confident that the current soreness is unrelated to the surgery or any structural issue. They chalked it up to a combination of overcompensation from a previous injury and Anthony's heavy workload last week.
Anthony missed games on Jan. 13 and 16 because of a sprained right ankle. He returned and played in two consecutive games last week that went into overtime, averaging 44:30 of playing time in those contests.
Fisher said Tuesday that Anthony might have been overcompensating on his left side because of the ankle injury.
"We're hopeful that it will calm down soon and he'll be back on the court soon," the coach said. "And if something tells us otherwise, we'll try to make a decision that's smart the way we've always tried to."
Information from ESPN's Mike Mazzeo was used in this report.