Former Irish striker said his international ex-team-mate and colleague at Sunderland could be a contender to succeed Giovanni Trapattoni when the Italian leaves his post
Quinn, writing for the Daily Telegraph, said Keane and the FAI would need to overcome their own personal history if the move was ever to happen. Keane has been outspoken in his criticism of the Ireland team at Euro 2012 in his role as a pundit with ITV.
"Roy does not accept mediocrity and Ireland’s performances in this tournament were mediocre at best," said Quinn.
He added: "That is what he was criticising, the idea that we were happy to accept those standards.
"It would take a huge leap of faith from both him and the FAI to appoint him, but also the fans he has railed against and the players he has criticised. But can he be the spark that ties it all back together and leads Irish football to redemption?" continued the former Arsenal forward.
Keane and Quinn fell out after World Cup 2002 during the infamous episode in Saipan. The Corkman later dubbed Quinn as 'Mother Teresa' but they patched up their differences within four years and the Dubliner hired Keane as manager at Sunderland in 2006.
"There is history between him and the FAI, but there was history between him and me before he accepted an offer at Sunderland and he did a great job for me there as manager.
"Just because there is history between them doesn’t mean they can’t resolve their issues and work together in the future," said Quinn.
Keane led the Black Cats to promotion from the Championship in his debut season and established the club in the Premier League before his departure in December 2008. A subsequent spell with Ipswich Town was less successful and he has been out of work since being fired by the Tractor Boys in January 2011.
The former Irish captain has said is eager to get back into management and has been linked with several vacancies. British bookmaker Ladbrokes have installed Keane at 25/1 to be the successor to Giovanni Trapattoni.
"He is available and if he sees a problem with the way Ireland are doing things, is he prepared to take the problem by the scruff of the neck and impose himself on it?" added Quinn.
In a 2002 interview with the Irish Times Keane said he would be interested in managing his country and quipped: "Nobody would play for me but we'd have great facilities!"
Quinn concluded that he was not suggesting Giovanni Trapattoni should be sacked from his position as Ireland manager but said the Irish Euro 2012 campaign must be analysed further.
"I agree Trapattoni’s position has to be looked at by the Football Association of Ireland and it will interesting to see whether he still has that hunger. We have to see whether there is still some life left in his reign," added the former striker.