The Republic of Ireland international has just over a year to run on his contract, fuelling speculation over his future.
Despite the talks being put on the back burner City boss Sven-Goran Eriksson remains confident of agreeing a new deal with Dunne.
"I really don't know where we are in terms of progress on Richard's contract but with six games to go I think it is more an end-of-season discussion," Eriksson told the club's official website.
"He has a contract for one more year so it is not a pressing problem. We don't want to lose him and I am quite sure he wants to stay here."