The Blues have lost a number of their long-serving lynchpins over the past several months, firstly allowing Jorginho to join London rivals Arsenal on deadline day in January.
Following their underwhelming 12th-placed finish in the Premier League last season, Mauricio Pochettino has allowed several other midfielders to move on, namely Mateo Kovacic, N'Golo Kante, Tiemoue Bakayoko, Ruben Loftus-Cheek and Mason Mount.
However, the Blues are yet to add any new lynchpins to their ranks ahead of the 2023-24 campaign, instead strengthening their attack with Christopher Nkunku, Nicolas Jackson, Angelo Gabriel and Diego Moreira.
As a result, the quintet of Enzo Fernandez, Conor Gallagher, Cesare Casadei, Andrey Santos and Carney Chukwuemeka have been deployed in midfield during pre-season, although the latter trio lack experience at the top level.
Chelsea are believed to have reached an agreement to sign Rennes' Lesley Ugochukwu for £23.2m, but the Frenchman is also only 19 years of age and may be loaned out to sister club Strasbourg for the 2023-24 season.
Ugochukwu could alternatively be integrated straight into the first team as an alternative to Brighton & Hove Albion's Moises Caicedo, whose £100m price tag could scupper a summer move to Stamford Bridge.
However, Spanish outlet Nacional - via Football365 - alleges that Chelsea are preparing an even more lucrative bid for Valverde, whose future with Real Madrid has been called into question recently.
The 25-year-old's Bernabeu contract is not due to expire until 2027, but the arrivals of Jude Bellingham and Arda Guler will lead to greater competition for places in Carlo Ancelotti's midfield.
Nevertheless, Real president Florentino Perez has rebuffed offers for Valverde so far this summer, with Liverpool reported to have made an €80m (£68.7m) approach earlier in the window.
Saudi Arabian duo Al-Ahli and Al-Hilal have supposedly come forward with bids of €100m (£85.9m), but their advances were also rebuffed, and it is unclear if Valverde has any interest in leaving Europe at this point in his career.
Despite their rivals' failed offers, the report claims that Chelsea are hoping to 'break down' Perez's resistance, and Valverde could be offered a quintuple-your-money contract by Pochettino's side.
The former Penarol youngster joined Real Madrid's Castilla outfit in 2016 and has gone on to make 204 appearances for the senior team, scoring 18 goals and setting up 15 more in the process.
Valverde - who can also play as a right winger - enjoyed his most productive season in front of goal during the 2022-23 campaign, banking 12 strikes and seven assists from 56 matches in all tournaments.
Chelsea take on West London rivals Fulham in their penultimate pre-season match on Sunday evening before concluding their United States tour against Borussia Dortmund on Wednesday.