Dunne has been linked with Tottenham and Newcastle United this month.
"The aim for every player here now is to stay at the club as long as possible and hopefully taste some real success. I am no different," Dunne told the Manchester Evening News.
"We all have to play a part and we all know if we do not perform to the best of our ability in training and matches that we might not be here that long in what looks like being an exciting future.
"The opportunity is there for any player who has been at this club a long time and knows how bad things have been at different stages, to grab the opportunity to be involved in good times.
"It is up to individuals to take that chance."