Jurgen Klopp’s side are embarked upon a project to rebuild their midfield options this summer and have already signed Carlos Mac Allister and Dominik Szoboszlai.
Now they are focused on adding a more defensively minded midfielder and Saints’ Lavia is high on their agenda.
Liverpool are exploring a swoop for Lavia, but Southampton value the midfielder at around the £50m mark.
Undeterred, Liverpool believe that they could negotiate a lower price with Southampton, who have been relegated from the Premier League and into the Championship.
It is unclear if Saints are willing to lower their asking price.
Lavia is also on Arsenal’s radar, but the Gunners are not in the process of making a move for his signature.
The 19-year-old was snapped up by Southampton from Manchester City only last summer, penning a five-year deal on the south coast.
He clocked regular Premier League football throughout Saints’ doomed campaign.
