The team finished ninth in the Eastern Conference this season, missing out on a place in the playoffs for the first time since the 2009-10 campaign.
The 29-year-old forward, who is due to become a free agent this summer, told ESPN: "I want to come back. But I also want to win. You know, me wanting to be here, if we can put ourselves in position to at least compete at a high level over the course of [the next contract], then I'm willing to stay here and I'm willing to ride or die for New York.
"You know, I've never once said I wanted to leave. I always said that I wanted to explore my options, I wanted to see what's out there.
"At this point in my career, it's about winning. Nothing else even matters. I don't know if I can afford to wait another season of losing. I really can't see that picture right now. This is not a decision that's going to happen overnight. It's going to take some time."
Anthony finished the season averaging 27.4 points per game, although he missed the last two games with a shoulder injury.