The Brazil goalkeeper has cut short his post World Cup holiday to travel to Merseyside where he will do the medical and sign his six-year contract with Liverpool.
Alisson will become the most expensive goalkeeper in history after Liverpool agreed a fee of £66.8m – almost double what Manchester City paid for Ederson last summer.
It will take Liverpool’s summer spending beyond £150m after already signing Fabinho, Xherdan Shaqiri and bringing Naby Keita after agreeing his deal last summer.
They could still move for Nabil Fekir but may decide to stop with Alisson.
The 25-year-old has also been linked with Chelsea and Real Madrid but Liverpool are in pole position and are confident of getting the deal over the line.
Chelsea wanted Alisson to replace Thibaut Courtois who looks set to join Real Madrid, but will now have to look elsewhere.
Alisson will replace Loris Karius as Liverpool No 1 after his double Champions League blunder.
Karius threw the ball at Karim Benzema who managed to divert it in and then dropped Gareth Bale’s long-range strike as Liverpool lost 3-1 to Real Madrid.
Jurgen Klopp went for Alisson early but Liverpool seemed to baulk at the figures before going back in this week.
Alison was always the top target but they did glimpse at Jan Oblak, who would have been even more expensive, before coming back in for Alisson.
As he walked through the airport heading for London he was approached by TV crews and said: “I want to thank the Roma fans. I’m sorry guys but I’ll have to talk later. OK?”
When asked about transfers and going all the way to August 9 trying to get deals over the line, Klopp said: “I don’t think so – I don’t hope so.
“Maybe something happens but it should not be the last day. I really thought the idea of moving the transfer window was good but only if we do it all together. In terms of squad planning, I am fine. In terms of football, we are in a good way but not where we want to be. A lot will come once the other boys are back.
“We will be fine at the end. At the moment, I am happy with the squad. Could something still happen? We will see.
“Big teams, successful teams – if you don’t buy it you have to build it. That means stay together, bring additions in and make the next step. That is how it is. The team and squad is in a really good moment.
“We had a situation last season where we had 12 fit players. They know we need the depth in the squad. They know we need quality and they know if we win something, we will win it with 25 players.”
When will Alisson make his debut?
Alisson is set to complete his transfer to Liverpool – but when will fans get to see him in action?
Alisson is on Merseyside to undergo a medical and complete his Liverpool move.
He is expected to complete his transfer in the next 48 hours and become the most expensive goalkeeper in the world.
However the Liverpool Echo report that he is unlikely to join his new team-mates on the pre-season tour of America due to the World Cup.
That would mean that his debut would be pushed back until August 4 when Liverpool take on Napoli in Dublin after a second training camp in France.