"I think Carmelo wants to play in New York, he wanted to come there, I think he likes playing in New York. I think he would stay in New York if he's got a chance to win," the Syracuse coach, whose team is currently 22-0 and ranked No. 1, told The Michael Kay Show on ESPN Radio.
Anthony is expected to opt out and become a free agent this summer, although his wife, La La Anthony, recently said she "definitely" expects him to stay with the Knicks.
"The problem in the NBA, your judged on winning championships," Boeheim said. "He's gotta try to go and play where they can win a championship or else he's gonna be failure, that's the bottom line."
Still, the Hall of Fame coach cautioned that all championship teams feature at least two great players and that the Knicks only have one.
"I'm not an expert on the NBA but everybody I've seen win an an NBA championship had a great player with him, whether it was Larry Bird, Magic Johnson, Michael Jordan, Kobe Bryant, they all had a great player with them," he said.
"I don't know if you can do it without that. I mean, David Robinson and Tim Duncan together. Tim Duncan had Manu Ginobili and Tony Parker. I think you gotta have that. I don't think you can win a championship without it."
Boeheim's comments echoed those of Kobe Bryant, who recently said the same thing while visiting New York.
Boeheim also said that Anthony is a scorer like Kevin Durant, not a playmaker like LeBron James, and that fans needed to understand that.
"Kevin Durant is a scorer, Carmelo Anthony is a scorer," Boeheim said. "They're different than LeBron James and, by the way, everyone else is different than LeBron James, too."
Boeheim watches the Knicks often and said they have been hampered by injuries to Tyson Chandler, J.R. Smith and Iman Shumpert. He believes they can still make a run. They are currently two games out of the eighth seed in the East.
"I think they're still capable of making a run here at the end," Boeheim said. "Obviously, you gotta get in the top six. You can't be eighth or seventh, right?
"If they can get into sixth or fifth so they dont have to play Miami or Indiana the first game, I think they can still do that. It's really having those guys healthy"
Adam Zagoria covers the New York Knicks and Big East hoops for NBA.com and SNY.tv. He also appears as a Big East Basketball Insider on SNY and 1050 ESPN Radio. You can follow him on Twitter and read his blog.