The Reds have already had a £37 million bid turned down for the 19-year-old but are preparing to launch an improved offer.
The Saints reportedly want around £50m for the Belgian who arrived at St Mary’s last summer from Manchester City.
Lavia earned rave reviews for his performances last season, making 29 Premier League appearances and scoring a goal.
However, the young midfielder is expected to leave this summer following Southampton’s relegation to the Championship.
Chelsea are reportedly planning to hijack Liverpool’s move for the 19-year-old.
The Blues, who attempted to sign Lavia for £50m a year ago, are prepared to table a higher offer than Liverpool.
But the good news for Liverpool fans is Lavia prefers a move to Anfield.
The Reds have had a busy summer transfer window, with Jurgen Klopp leading a big squad overhaul.
They have released Roberto Firmino, Naby Keita, James Milner and Alex Oxlade-Chamberlain.
Jordan Henderson has recently completed his transfer to Al-Ettifaq, while Fabinho looks close to moving to the Saudi Pro League.
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