The Albanian global has now established himself as Simone Inzaghi's number one and kept 17 clean sheets in his 53 appearances in all competitions last season.
According to Spanish newspaper AS, talks between Real Madrid and Roma are now at an advanced stage.
It is claimed the deal is so close, Alisson's Brazil teammates are aware he will be on the move.
Roma have allowed Alisson's agent Jose Maria Neis to speak to Madrid officials and a £61million fee could be agreed.
The 25-year-old Brazilian has emerged as Real Madrid's number one goalkeeping target this summer and the club are looking to make a move for him in the coming weeks.
Speaking to ESPN, Gab Marcotti said: "I think there is contract negotiation going on [between Roma and Alisson]".
Zero teaser featuring Salman Khan, Shah Rukh Khan released
But, laying these rumours to rest the maker of the film Ramesh Taurani claimed that the Race 3 would release as per norms in this overseas market.
Alisson has previously spoken of his hope to have his club future resolved prior to kick-off in Russian Federation and it appears increasingly likely that he will stay at Stadio Olimpico.
The player everyone expects to leave Stoke after their relegation from the Premier League is Shaqiri.
Liverpool may have missed out on a pre-World Cup move for Nabil Fekir, but are pursuing other avenues as they look to Stoke City's Xherdan Shaqiri.
"I can't tell you anything right now".
"We'll see if anything happens this week".
Liverpool visit Huddersfield Town at the John Smith's Stadium on the weekend before the third round of fixtures in Europe's premier club competition, scheduled for October 23 or October 24.
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