The 19-year-old joined the Saints from Manchester City for £12.5 million last year, and has impressed in his debut season.
The Belgian has stood out with his strong tackling and ability to win duels, making him a potential target for top clubs. According to The Times, the Reds and the Blues are monitoring his situation and may make a move during the summer transfer window.
Liverpool recently confirmed the departures of James Milner, Alex Oxlade-Chamberlain, and Naby Keita on free transfers, while Chelsea are expecting Mason Mount, Conor Gallagher, and Ruben Loftus-Cheek to leave this summer.
Both clubs are likely to strengthen their midfield, and Lavia would be an excellent long-term signing due to his tremendous potential.
Despite Southampton’s relegation, they could still demand a fee of around £50 million for the highly-rated teenager.
Manchester City have a buy-back option for £40 million, but it can only be exercised in the summer of 2024.