The fee is believed to be in the region of £66 million..
However in the past couple of days the rumours over an Alisson move have once against intensified and the Premier League side have now agreed a €75 million fee for the Roma keeper.
Italian website Forza Roma, which is affiliated to newspaper La Gazzetta Dello Sport, published a video which it said showed Alisson at Rome's Ciampino airport.
Real Madrid and Chelsea have also been linked with the 25-year-old.
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Liverpool made an initial offer last term £53M, with significant add-ons included, which was rejected by the Serie A outfit.
Another Brazil worldwide in Liverpool's sights is midfielder Bernard, who is also wanted by Arsenal and Everton.
The 28-year-old former England striker was expected to leave the club after being frozen out at Anfield last season and then made just six appearances after heading to West Brom on loan.
He has been on holiday after playing in all five of Brazil's fixtures at the World Cup in Russian Federation this summer before they were knocked out by Belgium in the quarterfinals.
Manchester City raised eyebrows past year when they shelled out £34.9million to sign Ederson from Benfica, a world record (in £) for a goalkeeper.