With Alisson having an excellent season for his club Roma last season, and representing Brazil at this summer's World Cup in Russia, he is thought to be attracting interest from clubs around Europe.
Liverpool were one of the main sides linked with signing the player as they look to strengthen in goal following Loris Karius's extremely disappointing Champions League final performance putting doubt over whether he could be trusted in goal in a season where Liverpool will hope to challange for the Premier League title.
The Italian outfit have reportedly put a £80 million price tag on the shot stopper, which is well above the price that the 'Reds' were willing to pay and so have ended their interest in bringing him to Anfield.
Real Madrid are also thought to be interested in the Brazilian, and with an injection of cash from their sale of Cristiano Ronaldo to Juventus, and so should the player leave the Italian capital that is thought to be his most likely destination.
Liverpool will probably still look to bring a goalkeeper in as competition for Karius and Simon Mignolet, with Stoke and England goalkeeper Jack Butland a potential target for Jurgen Klopp's side.