Southampton want £50 million for the youngster who had a breakthrough campaign in the Premier League last season.
Lavia made 29 Premier League appearances, becoming a fixture at the base of Southampton’s midfield.
He was superb last term but could do nothing to prevent them from suffering relegation to the Championship.
The 19-year-old has interest from the top flight and will likely move to a new club this summer.
Southampton director of football Jason Wilcox is leading negotiations for the south coast club and has placed a £50m price tag on the player.
Liverpool have already signed Alexis Mc Allister and Dominik Szoboszlai as part of their summer midfield drive, but they need more new additions.
The club are scouring the market for players to replace Jordan Henderson and Fabinho.
Henderson is moving to Al-Ettifaq to join former teammate Steven Gerrard, who manages the Saudi Arabian club.
Fabinho was due to move to Al-Ittihad, but The Athletic claims the deal is in jeopardy. However, there is an expectation that it will go through.
Fabinho is set to return to pre-season training tomorrow.
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