Welshman Allinson, 27, has yet to appear for Irish this season after the opening four rounds of the Premiership.
"I'm dying to get out on that field. It's a chance for a few of us who've not had much game-time to put our hands up," he told BBC Radio Berkshire.
Irish begin their Challenge Cup group at home against Agen on Saturday.
"If I get the nod to play, I'll be very much looking forward to it," Allinson said.
Tom Coventry's side, who have lost all their Premiership games so far, will also play Grenoble and Edinburgh in pool five.
Allinson, who has found himself behind Brendan McKibbin and Scott Steele in the competition for the number nine shirt, is looking forward to the challenge of facing European clubs.
"You get to go to France and teams like Agen and Grenoble are going to be really tough to face at home," he added.
"It's just a question of what sort of side they send over to play us. You know what French teams are like, you can't predict them, they're so unpredictable."
London Irish scrum-half Darren Allinson is hoping to stake his claim for a regular place when the Exiles begin their European Challenge Cup campaign.