"They might," he said after the Knicks' season finale Wednesday. "They might."
New York spoke to multiple teams about trades involving Anthony before the February trade deadline, and Anthony said Wednesday that he had seriously considered waiving his no-trade clause before the deadline.
"There was a point in time when I didn't think I would be back here," he said.
Anthony will meet with Knicks president Phil Jackson, general manager Steve Mills and coach Jeff Hornacek on Thursday to discuss his future as part of traditional player exit meetings.
Anthony said he would "love" to remain in New York but wants to make sure the club is committed to winning next season. The Knicks have lost at least 50 games in each of the past three seasons and might choose to rebuild the roster around Kristaps Porzingisrather than trying to win immediately with veteran imports, as they did this season.
"If everybody's committed to [winning], I'm committed to that too," Anthony said. "I want to win, and hopefully everybody else has that same type of mindset."
"To be honest with you, I don't know. I'll know more in the upcoming weeks or so," Anthony said. "I'm pretty sure the organization has an idea, a thought of what they want to do, how they want to do it. But at this point, it's all on me."
If Jackson tells Anthony the Knicks are looking to rebuild, the 32-year-old veteran said he would "respect it" and take that into account when deciding about his future.
"I have to figure it out at that point," said Anthony, who has two years remaining on the five-year, $124 million contract he signed in 2014. "It would have to be a decision I really sit down and think about and figure it out. I'm going to have to do a lot of figuring things out right now -- sit down with my team, sit down with my family, really figure this out, kind of really put what's important to me at this point in my career, which is winning."
He also said he looked forward to having direct communication with Jackson during his exit meeting. Jackson conveyed what many perceived as an indirect criticism of Anthony before the trade deadline, when he tweeted about a column that was critical of the 10-time All-Star.
Anthony acknowledged that it was "hard to trust" Jackson after the team president's veiled criticisms earlier in the season.
"If somebody was talking bad about you indirectly at your job, what would you do? You would feel a certain way," Anthony said. "You would want that person to come straightforward with you. And I feel the same way. I'm always open. I'm a very honest person. I know the business and I know the game and I know how it works. So if it's something that you want to get across, a message that you want to get across, I've always been open."
The veteran forward said he thought the Knicks may ask him to change his role during the exit meeting, whether that meant a reduction in minutes or a new role as a reserve.
Anthony said he had to be "prepared for anything" going into the meeting. But he made it clear that he had no plans to accept a bench role.
"Come on, man," he said. "We don't even have to go through that."
Anthony ended up playing in the Knicks' finale after Hornacek said he assumed the forward wouldn't a day before. Anthony said he always had planned to play against the76ers, contradicting his coach.
He didn't play in the fourth quarter of the contest, but fans at Madison Square Garden chanted, "We want Melo," in the closing minutes.
"It felt good. It's been a while," said Anthony, who had been booed at times during the season. "It's been a while to sit there and hear that."