The Blues have made a £48million bid to hijack Liverpool’s move for the Southampton midfielder.
Saints are thought to want £50m for the 19-year-old but Chelsea’s offer is higher than any of the Reds’ three rejected bids.
The Blues also remain in the hunt for Brighton’s £100m-rated midfielder Moises Caicedo.
New manager Mauricio Pochettino has been tasked with a total rebuild following the departures of senior midfielders Jorginho, Mateo Kovacic, N’Golo Kante and Mason Mount.
Enzo Fernandez arrived for a Premier League record £106m in January but Conor Gallagher is his only senior partner as things stand – and the academy graduate could yet be sold.
Teenager Carney Chuckwuemeka, who arrived from Aston Villa for £20m in 2022, is another possible option after impressing in pre-season.
However, Chelsea co-owner Todd Boehly looks set to flex his financial muscles instead, having already spent close to £1billion in 15 months.
If he meets the asking price for Caicedo and Lavia, the Blues could field a midfield worth around £256m.
Real Madrid are the only club that come close to matching that value with Jude Bellingham (£114m), Aurelien Tchouameni (£85m) and Luka Modric (£35m) costing a combined £234m.
In the Premier League, Manchester United’s midfield of Paul Pogba (£89m), Fred (£52m) and Bruno Fernandes (£67m) was worth a total £208m.
It means that if successful in the coming days, Chelsea will have the most expensive midfield ever assembled.