The 25-year-old has been at Roma for two years after starting his career at Brazilian side Internacional.
Liverpool boss Jurgen Klopp was forced to defend goalkeeper Loris Karius last week after another mistake – this time in a pre-season friendly against Tranmere.
The 25-year-old German spilled a free-kick that allowed the hosts to score in Liverpool’s 3-2 win at Prenton Park.
Karius was at fault for two goals in Liverpool’s 3-1 defeat by Real Madrid in the Champions League final, but it was later found to have suffered a concussion.
Alisson played all five games, keeping three clean sheets, as Brazil were knocked out at the quarter-final stage of the World Cup by Belgium.