Over the past 24 hours, the two Big Six sides have engaged in a gripping transfer tussle for the signature of Brighton & Hove Albion's Moises Caicedo, who was the subject of a successful £110m offer from the Reds.
However, as Liverpool were preparing to welcome Caicedo to Kirkby for a medical, they were allegedly informed that the Ecuadorian only wanted to join Chelsea, with whom he has already agreed personal terms.
While Chelsea have supposedly still not tabled a bid to Brighton's satisfaction, the Blues are thought to be edging closer to a £115m transfer, dealing Liverpool another blow in their search for a new number six.
Should Liverpool fail in their efforts to poach Caicedo, the Reds will be expected to accelerate their pursuit of Lavia, but Chelsea could apparently still try for the Belgian regardless of the outcome of their attempts to sign Caicedo.
Southampton have already rejected three insufficient Liverpool bids for Lavia, who is said to be valued at £50m by the Saints, as his contract does not expire until the summer of 2027.
The Reds had initially failed to meet Southampton's asking price, whereas Chelsea are alleged to be readying a £55m approach, which should be accepted by the Championship club.
However, talkSPORT claims that Jurgen Klopp's side are prepared to lodge an identical offer, as the Reds fight tooth and nail to bring Lavia to the club as Fabinho's successor.
Liverpool have been left extremely thin on the ground in midfield due to summer exits, as Fabinho, Jordan Henderson, Naby Keita, Leighton Clarkson, Alex Oxlade-Chamberlain, James Milner and Arthur are no longer at the club.
Thiago Alcantara and Stefan Bajcetic are also yet to recover from the injuries that ruled them out of the business end of the 2022-23 season, seeing Klopp start with Alexis Mac Allister, Dominik Szoboszlai and Cody Gakpo as his midfield trio against Chelsea on Sunday.
Liverpool came through that opener with a point to their name from a 1-1 draw, but their lack of a defensive midfielder was evident, as Chelsea created numerous chances to take all three points at Stamford Bridge.
Lavia left Manchester City in 2022 after making just two appearances for Pep Guardiola's side, but he shone for Southampton in his debut campaign with one goal and one assist from 34 games.
However, the 19-year-old's efforts were not enough to save Southampton from the drop, and he was an unused substitute in their Championship opener against Sheffield Wednesday before sitting out their subsequent meetings with Gillingham and Norwich City.
Man City are understood to have inserted a buyback clause into Lavia's contract when he departed for St Mary's, but that £40m option does not become active until 2024.
Liverpool return to Anfield for the visit of Bournemouth next weekend, before Chelsea tackle West Ham United away from home in a London derby on August 20.