Nasri's future has been the subject of conjecture this summer after he entered the final year of his contract at Arsenal.
City have been strongly linked with the France international whilst Manchester United have also been mooted as potential suitors.
On Saturday, Mancini made no secret of his wish to bring Nasri to Eastlands. He said: "I hope that this player can arrive before the end of the month."
And Wenger - who recently insisted Nasri, along with Cesc Fabregas, will be remaining at Arsenal - has reacted angrily to the comments.
Speaking after his side's 1-1 draw with Hangzhou Greentown, he said: "I think the comments are not allowed. They are against the basic rules of football and he should be informed [of that].
"I don't know what should be done. I don't spend my time worrying about what other people say because we are focused on our game.
"What we want is respect and we don't make these comments about players who are under contract at other clubs.
"Disrespectful? I cannot say otherwise. This comment is absolutely out of order but I don't give it more importance than that."