Sir Alex Ferguson confirmed on Tuesday that the England striker would not sign a new contract at Old Trafford and many see Eastlands as his most likely destination.
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Asked if there had been contact between City and the player, Mancini said: "No. Never."
Mancini echoed the comments of Real Madrid boss Jose Mourinho, who said on Tuesday night that he expected the player to stay where he is.
"Rooney is a great player but I think he'll stay at United," said Mancini. "He's a good player, he's an important player for United."
Pressed on whether he would be keen to sign the striker, the former Inter Milan boss added: "He is a United player. It's not correct to speak about that situation.
"I have respect for him, for Ferguson, for United. I want to speak only about my players.
"It's not my problem. I'm City manager. I have a lot of problems with my players. It's important for me to focus on Thursday's game (against Lech Posnan in the Europa League).
"He is a strong player like (Fernando) Torres, like (Lionel) Messi, like Carlos Tevez, like (Mario) Balotelli. This is my opinion."
Source: PA
Source: PA