Signing a new goalkeeper has become something of a priority for Liverpool manager Jurgen Klopp following the disastrous performance of current first-choice Loris Karius in last month's Champions League final.
The five-time winners face Austria in their final warm-up match on Sunday before they take on Switzerland in their opening Group E game on June 17.
Liverpool FC have been linked with a move to sign AS Roma's Brazil global in recent months.
Firmino said: 'Every once in a while I give him a pinch to come to Liverpool to help us and such, but it's with his agents.
The Reds have already signed another of his compatriots, Monaco midfielder Fabinho, in a £39 million deal, with the 24-year-old explaining how Firmino's influence was key.
Firmino and the 25-year-old keeper have linked up ahead of the World Cup in Russian Federation and Liverpool supporters are hopeful that the attacker can persuade the goalie to come to Anfield, the same way he did with Fabinho.
Firmino is now with the Brazil squad and according to the man himself, he's been trying to nudge Alisson in the direction of joining Liverpool. I know he's a fantastic person, his background is from nice people.
If he can play a role in any deal to bring Alisson to Anfield, his popularity would only increase.
Liverpool loan Ovie Ejaria to Rangers
Liverpool youngster Ovie Ejaria has joined Rangers on a season-long loan, the Scottish side have announced. He spent the second half of last term on loan at Sunderland , featuring 11 times in the Championship.
Princess Charlotte comforted by Kate Middleton as she cries
The head of state, who travelled in an Ascot Landau, wore a sky blue coat and dress by Stuart Parvin, and a hat by Angela Kelly. Guardsman Charanpreet Singh Lall marched among 1,000 British soldiers who took part in the Trooping the Colour parade .