"That is something that is huge for us. Every nation in the tournament will be discussing us having the likes of Gareth with us," Allen, who plays for Liverpool in the Premier League, told British media.
"I think he is a real standout player in the tournament. We are hoping to strike as much fear into everyone as we can in terms of that."
Allen, who has made 25 appearances for Wales, has overcome a knee injury picked up during his country's pre-tournament training camp in Portugal.
The 26-year-old dismissed comparisons with midfielders Andrea Pirlo of Italy and Spain's Xavi, for which he was given the nicknames "the Welsh Xavi" and "the Welsh Pirlo".
"I'm just an Average Joe. It's a dangerous one because I had 'the Welsh Xavi' tag for a while and that didn't really do me too many favours. So I'm trying to steer myself away from the new one too," Allen added.
Manager Chris Coleman's men open their Group B campaign against Slovakia in Bordeaux on Saturday before facing England and Russia.
(Reporting by Ian Rodricks in Bengaluru; editing by Clare Lovell)
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