Twice a play-off finalist at the home of football, the Dubliner has suffered deep-seated disappointment on the revered turf on each occasion.
It is not hard to fathom why the conventional route to promotion holds much more allure to the 27-year-old than another visit to north-west London and a potential unwanted treble.
The only time he wants to put in a Wembley appearance is just two days after the Championship play-off final when Ireland take on Roy Hodgson’s England in an international friendly.
But Quinn is savvy enough to appreciate that his chances of donning the green jersey for the senior Republic side for the first time is unlikely under Giovanni Trappatoni, who has overlooked him time and time again.
For the former Blades driving force, who has proved one of the Championship bargain buys of the season after Steve Bruce signed him in August, domestic matters take precedence. Clinching a top-two spot and avoiding the dreaded end-of-season lottery is the name of the game.
Quinn is set to start for the Tigers in today’s encounter with Middlesbrough at the KC Stadium after making his return from the bench in Tuesday’s defeat to automatic promotion rivals Watford following a knee injury.
He still carries the mental scars from last season’s shattering penalty shoot-out loss with the Blades against Huddersfield Town in the League One play-off final.
He was also part of the United line-up which lost to Burnley in the Championship showpiece in 2008-09.
On both occasions, Quinn and his Blades team-mates had automatic promotion in their grasp coming into the final weeks of the season.
Exactly 12 months ago today, the Blades were two points ahead of city rivals Sheffield Wednesday in the second automatic promotion position in football’s third tier, only for the Owls to end the campaign as runners-up, finishing three points above their arch-rivals.
This time around, Quinn and his Tigers team-mates hold a one-point advantage over third-placed Watford and negotiating the final six matches and getting over the line in second would mean the world to Quinn.
He told the Yorkshire Post: “I don’t think I have the heart for the play-offs again. I have lost two finals and it would make a change if we went up automatically straight away and avoided them.
“It is a bit of a motivation for me, although I think the lads don’t want to be there, either. In my eyes, the best way to go up is automatically.
“A lot of people think it is through the pay-offs. But there is such a fine line between success and failure there, as I saw last season, which was heart-breaking.”
Quinn played 15 games in the top flight with the Blades in 2006-07 – a season which will forever be remembered by Unitedites for the Carlos Tevez affair, which cruelly robbed them of their Premier League status.
Given that, it is perhaps not surprising that Quinn feels he has unfinished business at the top table.
Quinn said: “It would be massive to get promoted back to the Premier League. In the past couple of years, I never thought I would be facing this because of how things went at Sheffield United.
“I was on the crest of a wave when I was playing there at 19 and 20 and didn’t realise how good it was and how well I had it.
“Now that I am 27 and all those years have passed, I appreciate it is so tough to get out of these leagues and some top, top teams are trying to get back to the ‘Promised Land’. It would be phenomenal if we get there. I would relish playing there again.”
In that part of the campaign commonly referred to as ‘squeaky-bum time’ by all and sundry, Quinn insists he and his City team-mates will be approaching a seminal month with a positive smile.
It is what you would expect from a side managed by Steve Bruce, who throughout his glory years playing at Manchester United was well versed in coming out on top during pivotal end-of-season denouements.
Quinn said: “It has been a great season and we thoroughly deserve to be up there and just need to take it on.
“We always felt we had a chance. From day one, when I came to training, the lads were unbelievable and always pushing each other. It is such high quality; Matty Fryatt said when he came back training the other day, he couldn’t believe how high the standard was.
“For me, it has probably been the most enjoyable and best season of my career. I am at an age where I am under no pressure and enjoying my football and the manager says the most important part is enjoying it, because if you don’t, you don’t play well.”
While the most consistent campaign of his career may yield a cherished promotion, Quinn’s hopes of making his international debut appear further away than ever, despite his manager championing his cause.
Quinn is justifiably entitled to think there is not a lot more he can do to earn a call-up for his country. Yet if it somehow did come, it would mean everything to him.
Quinn, whose brother Alan was capped eight times by Ireland, said: “I always think about Ireland, especially when the international breaks come up and if I will get that nod or not.
“But I am not sure I will now because of this manager here as he has not put me in during all his years there.
“I don’t know if I am his type of player, which is sad because I would give my left foot to play for Ireland, even if I had to hobble around on my right!”
“I am very disappointed that over the years he has never given me a shout for even a friendly or meet-up for a training squad, just to show him what I am capable of.
“If he goes, maybe a new manager will come in and I can try and impress him.”