The 28-year-old defender has been named City's Player of the Year for the last 4 seasons and was offered a new contract as there is only a year left on his current deal.
Dunne turned down the offer amid the confusion surrounding the managerial position but with Sven-Goran Eriksson having now left the club and Hughes swiftly appointed as his successor, the former Blackburn boss is hoping to persuade Dunne to sign a new deal.
"I've spoken to Richard, he's on holiday abroad at the moment but I've had a discussion with him and I've told him my feelings on the situation," Hughes told the City website.
"Obviously I'm very keen for him to remain at the club, and we're working in that direction.
"It's a little bit difficult because he's away at the moment, but I'm sure that when he's back this will be resolved very quickly.
"We have offered Richard a substantial deal, there may be more negotiations to be done but I am very hopeful that he will continue to be a Manchester City player.
"He's been outstanding at City, he's key to what we are trying to do here and if we can, we'll make sure we do everything we can to keep him."
Hughes played alongside the Republic of Ireland international at Everton in 2000 and feels he is under-rated outside the club.
"He does not shout about himself from the rooftops, he does not do that much press apart from what he has to as our captain," he added.
"There are some players out there who promote themselves more but the key is what you do on the pitch, and he has been outstanding in that respect."