The midfielder has impressed in recent weeks as injuries have hit the Reds.
The Welshman has endured a difficult spell at Anfield since joining from Swansea City in 2012 as one of Brendan Rodgers' first signings.
He has enjoyed something of a renaissance under Jurgen Klopp in recent weeks though, putting in a series of impressive performances.
He now has a chance in the Liverpool first-team following injuries to Emre Can and Jordan Henderson, and Wright says he hopes the midfielder gets his chance to impress as he could offer something to the side.
“He’s been there three and a half years now and you’re thinking to yourself, he’s got to start doing something,” he told Match of the Day 2.
“With someone like him, you’re hoping that he can get a chance, with Jordan Henderson and Emre Can out injured.
“You feel that with Henderson and Can it may be hard for him, but when he plays like that [against Bournemouth] then he might be able to do something.”
Allen will be hoping he can get a run of games in the side to try to secure himself a regular spot in the future.
He certainly has an incentive to do so, with him having just a year left on his contract and keen to try to secure himself a new deal at Anfield.
Much is likely to rest on the work that Liverpool boss Klopp does in the summer transfer window, as several new arrivals could see him pushed further down the pecking order.