Giovanni Trapattoni's players will reportedly share a bonus of 4million Euros - around £3.4million - if, as expected, they complete a play-off victory over Estonia at the Aviva Stadium on Tuesday night.
However, when the final whistle sounds, Dunne insists his bank balance will be the furthest thing from his mind.
The 32-year-old Aston Villa defender said: "We all make enough money at our clubs and playing for Ireland is an honour, it's not about money.
"The whole country will benefit from it and the main thing is having the pride. Going out and playing in the finals is all that matters to the players.
"There's nobody in the world who can give you £3million or £4million, and you finish third in your group. It's of no benefit to anyone.
"Footballers want to play in tournaments and this is a really big tournament. To go and represent Ireland in it is going to be something that money can't buy."
Dunne is one of the few members of the current squad to have been to a major tournament, although he did not play at the 2002 World Cup finals, the last one for which they qualified.
His hunger to address that gap in his curriculum vitae is therefore understandable.
He said: "I would love to. It's probably the pinnacle of the game.
"Apart from the World Cup, the European Championships is as high as you can play in, so to have the opportunity to play against the top sides in a competition, it would be a very proud moment for us all.
"It's pleasurable for all of us. We all have to savour the moment because the likes of myself and Shay [Given] and Damien [Duff] and Robbie [Keane] know it doesn't come around very often and it may not happen again for a few of the lads."
Should Ireland complete the job tomorrow night, they would reach their first European Championship finals since 1988.
Dunne was a schoolboy during that tournament, but remembers only too well the excitement it created.
He said: "I remember watching the games sitting in the house. The same as every kid, I would probably watch a bit and then run out and have a game of football and run back in.
"It was brilliant. The lot of us grew up watching the World Cups and the Euros when we were qualifying, and to go and do it is going to be strange, but really good."
It was Jack Charlton who took the Republic to that tournament as he established them as an unlikely force, and by following suit, Trapattoni is in line to win the contract extension he is seeking amid speculation he will be offered a new two-year deal.
In Dunne's eyes, that would be well deserved.
He said: "His record speaks for itself. In the campaigns before he came, we probably weren't looking like we were going to qualify and this time, we have always been in with a good chance of getting to a play-off or topping the group.
"He has built the squad over the last four years, so I think he can carry on and hopefully get us to the World Cup."