"He has not promised me anything, but I'm quite sure it will be sorted out," said the City boss.
Dunne, 28, who picks up around £28,000 a week, wants a hefty pay rise to put him level with the club's top earners and reflect his standing as City's best player in recent years. Eriksson added: "He is 28 and you might only sign one or two more contracts. So you want a long one of three or four years.
"He has become a special, special player for us. He has been the best player for the club for the last couple of years and he was Ireland Player of the Year.
"It's easy to see why we want to keep him."