The Queens Park Rangers defender believes that Ireland will benefit if the Toffees qualify for the Champions League and says that Coleman should remain at Goodison Park
Roberto Martinez's side are on course to qualify for Europe's premier club competition, sitting in fourth place, two points ahead of rivals Arsenal, and Dunne thinks that the former Sligo Rovers defender would be better served remaining at a club where he is thriving.
"If they get into the Champions League, then I don’t see why not," Dunne told reporters.
"It’s a great club although it does not have the financial backing of Manchester City or even Manchester United. But he’s playing every week, he’s a first choice and his form is brilliant so there is no real reason for him to go looking for stuff elsewhere."
The Queens Park Rangers defender added that playing Champions League football would improve Coleman and suggested that Everton would have to fight off the attention of potential suitors, should the 25-year-old continue his upward trajectory.
"He’s been great and if he can get into the Champions League it will improve him again," said Dunne. "The only worry that Everton will have is that the bigger teams will try to take him."
In addition, Dunne believes that Martin O'Neill's Republic of Ireland team will benefit should Everton make it into the Champions League, with James McCarthy, Aiden McGeady, Darron Gibson and Shane Duffy also at the club.
"I think the Ireland team will feel the benefit," added Dunne. "And if Everton get into the Champions League then that will help them as well."
"But I think the team will evolve and Martin will bring a lot of new players in and it will progress."