The pair were involved in an incident last season while Garnett was still with the Boston Celtics, which threatened to boil over off the court.
"I don't have no problem with him. He don't have no problem with me. We talk. We laugh. We joke. I see him out and about. No problems," Anthony said, the New York Post reports.
Garnett and the Nets avenged their heavy defeat earlier this season to the Knicks with a win over their city rivals at Madison Square Garden on Monday night.