Reds boss Jurgen Klopp made Roma's Brazil international custodian his top target in this summer transfer window after Loris Karius' Champions League final nightmare, while Simon Mignolet also seems to set to depart Anfield after falling down the pecking order.
However, the German's pursuit of Alisson now looks destined to end in disappointment after Roma president James Pallotta revealed on Thursday evening that the player is close to joining the European champions in a deal close to £70million.
Liverpool could now make a move for Atletico Madrid's Slovenia international custodian Jan Oblak, although they will possibly face stern competition from Paris Saint-Germain for his signature.
Meanwhile Burnley's Tom Heaton has also been linked after the Clarets shot-stopper lost his first-team place and England World Cup spot to team-mate Nick Pope.
The 32-year-old was number one at Turf Moor until he suffered a shoulder injury last September and that handed Pope a chance to shine.
The 26-year-old subsequently impressed Clarets boss Sean Dyche so much he continued to keep Heaton out of the side after his return to fitness in February, while also claimed a place in England boss Gareth Southgate's 23-man squad in Russia.