The relegated club are thought to want £50m for the Belgium international while Liverpool have a valuation of the 19-year-old based on his age and experience.
Lavia has played 29 Premier League games for Saints while Liverpool bought the 24-year-old World Cup winner Alexis Mac Allister from Brighton for £35m and the Hungary captain Dominik Szoboszlai for £60m this summer.
However, Liverpool’s need for a defensive midfielder has become more pressing after the sales of captain Jordan Henderson and Fabinho to Saudi Arabian clubs Al-Ettifaq and Al-Ittihad.
Manager Jurgen Klopp confirmed on Tuesday that he is looking to strengthen his midfield, saying: “It is no secret we are still looking for players to join us” and stating Liverpool do not have a “proven No 6” in their squad anymore.
Liverpool have also considered Bayern Munich’s Ryan Gravenberch and Manchester City’s Kalvin Phillips while they have been linked with Fluminese’s Andre.
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