The former MVP will not make a pitch to the New York Knicks star.
The Bulls will meet with Anthony when free agency opens on July 1, ahead of the Mavericks, Rockets and Lakers, but Rose, a former MVP, told Yahoo Sports it is "not his job" to recruit other players.
"My thing is if they want to come, they can come," Rose said.
He was, however, very complimentary about Anthony's game and said he believes they could play together.
"I love Melo's game," he said. "He's a great player. Takes the game serious, he's consistent, he shoots the ball great. I love his heart.
"I can play with anybody, no matter who it is. I believe I can play with anyone if they step on the court with me."
Some of Anthony's other suitors are bringing out the big guns as they look to persuade him to join their team. The Mavericks' Dirk Nowitzki will make his pitch to Anthony as he has done with other big-name free agents that Dallas have tried to recruit in recent years.
“For sure, if Dallas is on his radar, we’ll talk," Nowitzki said. "He’s one of the best scorers in this league. He can score with the best of them. If that’s where he wants to be, we’d love to have him.’’
Los Angeles Lakers star Kobe Bryant has already spoken to Melo on the phone about them playing together in LA, and he plans to meet the small forward again next week.
Anthony maintains an offseason home in Los Angeles, and if he is to leave the Big Apple the Lakers would offer him another huge market.
The best fit still appears to be the Bulls, however. Anthony is looking to be in position to win an NBA title in the near future, and a move to Chicago to play with a healthy Rose would put him on a championship-caliber roster for next season.