Lavia has been identified as a top target for the Reds' midfield revamp, following the arrivals of Alexis Mac Allister and Dominik Szoboszlai. The 19-year-old is reported to be the man Jurgen Klopp and the club hierarchy are looking at to add depth to the 'number 6' position.
However, talks appear to be at an impasse between the two clubs, with Neil Jones reporting that there's currently "no agreement" with Southampton over the player's valuation, which Liverpool currently see as too high.
The journalist told Empire of the Kop: "The real problem Liverpool face in this deal is the price of the player and the price that Southampton want.
"The last I heard, which was late last week, was that it was too high. They don’t view him as £50m investment at this stage; it would be a lot less than that."
While it seems Liverpool are not prepared to go big on Lavia, they are not the only ones interested.
It is said that Chelsea's first choice signing is Brighton's Moises Caicedo, but they view Lavia as a backup if that deal falls through. Arsenal and United's interest depends on outgoings at each club.
Meanwhile, Southampton — who are resigned to losing Lavia this summer — have already moved to agree a deal for a replacement in Manchester City and Northern Ireland midfielder Shea Charles, who is set to undergo a medical ahead of a £15m deal.
Despite their apparent hesitancy to meet Southampton's demands, it seems Lavia very much is a player Klopp and the club rate. Other recent reports, including from Sky reporter Florian Plettenberg insist that Lavia is a player Klopp "wants", while Fabrizio Romano — who previously suggested the Reds could get "creative" in working out a deal for the midfielder — told Born and Red: "All the people at the club believe this boy is a very special player, but it is true that he is not the only one on the list.”
Who the other players on the list are is unclear, with Liverpool seemingly having ended their recent interest in Khephren Thuram.