The former Cardiff Blues scrum-half has not pulled on the Three Feathers since the 2006 Under-19 World Cup in Dubai.
But he will work closely with Edwards, who has become the Exiles defence coach alongside his Wales duties.
“The sooner I can get involved the better because that’s (international honours) something I aspire to do,” said Allinson, who made 25 appearances for Irish last season.
“I spoke to Brian Smith about it and he believes I can do it this year.
“He’s given me a few things to focus on so I’m going to go away and work hard and hopefully that will lead me on to an international cap.
“I haven’t heard anything off Gatland but it will be interesting to see because Shaun is going to be up with us so hopefully having him there will be a little nudge through the door as he’ll be working with us – as I say hopefully sooner rather than later because it’s something I want to do.”
Allinson came through the Blues ranks and spent three seasons with the senior side.
He made 29 appearances for the capital city outfit and was a major part in their march to Amlin Challenge Cup glory in 2009.