Liverpool have stepped up their search for a new shot-stopper following Loris Karius's high-profile errors in the Champions League final, with the German gifting Real Madrid two goals in a 3-1 defeat.
Alisson has been regarded as Liverpool's number one choice for a number of months now, but Roma are determined to keep the 25-year-old.
The Guardian reports that the Italian outfit have no plans to sell the Brazil international before this summer's World Cup, and would demand at least £79m before they consider letting him go.
That fee would be a new record for a goalkeeper, surpassing Manchester City's purchase of Alisson's compatriot Ederson last summer.
Alisson, who is above Ederson in the Brazil pecking order, has also been linked with a move to Real Madrid, but Roma are still hopeful of keeping him at the Stadio Olimpico and plan to offer him a new deal.