Eight Welshmen have lifted the most coveted prize in Welsh rugby previously, the last Gareth Thomas with Toulouse in 2005.
But Byrne will go head-to-head with Gethin Jenkins for a place in history when Clermont Auvergne take on Toulon at the Aviva Stadium.
“It’s not many Welshman who have managed this,” said Byrne.
“It would be nice to get into that prestigious club but we’ll have to wait and see.
“It’s massive (for Clermont), especially after losing last year in the semis. We sat down as a group and it surprised me how much the French boys want to win Europe.
“You hear stories that the French title is more important but everybody wants the Heineken Cup just as much you know.
“We want to be the best team in Europe not just in France.
“Toulon are full of international players so it is going to be difficult. We’ve played them twice this season, we beat them the first time at home and drew the second away.”
Byrne is well aware of the threats Toulon pose and with Jonny Wilkinson in their ranks, discipline is chief among them.
The former England star was instrumental in the Cote d’Azur club’s quarter and semi-final wins and Byrne admits Clermont can not afford to be ill-disciplined.
“We can’t give away penalties in our half because it is almost guaranteed to be three points,” added Byrne.
“We’ll be squeaky clean.”
Byrne recently missed out on selection for both the British & Irish Lions and Wales, as Robin McBryde opted for a youthful squad.
But he has not given up hope of winning further international honours.
“We were training when the Lions was announced but I wasn’t expecting to get picked. There were a lot more disappointed boys out there than me.
“I then had a phone call from Robin McBryde saying Wales were going to take a young team out there. I was available but I wasn’t needed.
“It’s a hard one. I’ve been involved in the last two squads and haven’t played a game. I haven’t given up hope but I will see as time goes on.”
Welsh Heineken Cup winners: Tony Rees (Brive 1997), Ieuan Evans (Bath 1998), Nathan Thomas (Bath 1998), Richard Webster (Bath 1998), Allan Bateman (Northampton 2000), Andy Newman (Northampton 2000), Rob Howley (Wasps 2004) and Gareth Thomas (Toulouse 2005).
