The Reds have been heavily linked with a move to try and sign the 25-year-old Brazilian goalkeeper as Jurgen Klopp ponders bolstering his options between the posts for next season.
Neither Loris Karius nor Simon Mignolet have been particularly impressive this term and the Reds could well be looking to add to their goalkeeping options.
AS Roma star Alisson has been widely touted as a possible target for the Merseyside club as the summer transfer window draws ever nearer.
However, AS Roma director of sport Monchi has insisted that the Italian club currently have no plans to entertain any offers for the highly-rated shot stopper.
Speaking in an interview with Italian outlet Mediaset Premium, Monchi said: “All our players can do even better, including Alisson.
“I am honestly a little tired of talking about Alisson’s future, as I get asked this in every interview now.
“We have not received any offers and have no intention of selling. We are happy to have Alisson, we want to enjoy him.
“I don’t want to name a hypothetical price-tag for him, because when someone doesn’t want to sell, he doesn’t name a price.”
Meanwhile, Liverpool FC are currently gearing up for their crunch showdown against Manchester City in the first leg of their Champions League quarter-final clash on Wednesday night.
The Reds, who are third in the table, warmed up for the game by coming from a goal down to beat Crystal Palace 2-1 at Selhurst Park on Saturday thanks to goals from Sadio Mane and Mohamed Salah.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news