The 24-year-old’s father, Carlos, who acts as his representative, arrived at the weekend for talks regarding the World Cup winner’s future.
It is understood the Argentina international has a release clause, believed to be between £45million and £55m, in a contract he only signed in October and Liverpool are close to triggering that.
Seagulls boss Roberto De Zerbi admitted last month he is already resigned to losing a player who was key in securing their first European participation with a sixth-placed finish in the Premier League, just five points behind Liverpool.
Jurgen Klopp is looking to rebuild a midfield which misfired this season and Mac Allister has been a long-term target, with James Milner, Naby Keita and Alex Oxlade-Chamberlain departing at the end of their contracts.
Liverpool were also interested in Mason Mount, entering the final 12 months of his contract at Chelsea, but Manchester United appear to be the front-runners and Klopp does not want to get into a protracted – and often expensive – process so has moved on to other players.
The Reds have been linked with Bayern Munich’s Ryan Gravenberch, Nice’s Khephren Thuram and Borussia Monchengladbach’s Manu Kone and will be looking to get their business done early in time for the start of pre-season on July 8.