Roma are willing to lower their asking price for Alisson, according to reports in Italy.
The goalkeeper has been linked with a transfer to the Premier League this summer with Liverpool and Chelsea mooted as suitors.
Liverpool need a new No.1 as questions about Loris Karius's suitability for the role continue to mount.
Chelsea are preparing for the departure of Thibaut Courtois and have ear marked Alisson as the perfect replacement.
Roma were demanding upwards of £70million for Alisson, but GianLuca Di Marzio.comclaim the club have softened their stance.
The Italians are willing to knock off almost £9m from the asking price and there is hope Roma could be convinced to sell at an even lower figure.
The news may prompt Liverpool to re-ignite their interest in Alisson after originally balking at Roma's asking price.
Liverpool made enquriries about Alisson at the start of the summer, but cooled their interest because of Roma's insistence no offer lower than £70m would be considered.
Chelsea are about to appoint a new head coach and usher in a new era under Maurizio Sarri, and the former Napoli boss is thought to be an admirer of Alisson.
The Brazil No.1 impressed for his country at the World Cup, but is now free to discuss his club future after exiting the tournament at the quarter-finals stage.
Roma are still hopeful a bidding war will erupt between Chelsea and Liverpool for Alisson's services.
Alisson did want to move to Real Madrid, but the La Liga side too have backed away from a potential deal.
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