In the wake of his sides Euro 2012 failure, rumours have begun to circulate concerning the futures of senior players such as Shay Given, Damien Duff and Dunne. Another of the old guard, Robbie Keane has announced that he will continue to play for his country, ahead of the World Cup 2014 qualifying campaign.
With players such as James McClean, James McCarthy and Darron Gibson set to be blooded at international level, Trapattoni has called for irreplaceable Dunne to consolidate his position in the Ireland side for years to come.
The Italian admitted to asking the Aston Villa defender not to retire, but conceded that the player's family could sway his decision.
“He smiled, but I have to convince him," Trapattoni said. "Sure, there is a possibility that he will speak to his family, but in this moment we need Dunne again.
“We don’t have another like him. Maybe we have options in place of Damien Duff, but with Dunne, we need him in his position.”
After three consecutive defeats in the group phase of Euro 2012, Ireland will look to reach back-to-back major tournament finals as they kick off their World Cup 2014 qualifying campaign with a trip to Kazakhstan in September.