Despite enjoying a relatively solid campaign through a ninth-placed finish in La Liga and only losing the Copa del Rey final on penalties, Valencia made the decision to part ways with head coach Jose Bordalas.
Gennaro Gattuso has been appointed in his place, the Italian now tasked with trying to earn a return to European football during his stint at the Mestalla.
If reports are to be believed, Valencia must raise significant funds through player sales this summer, a scenario which may lead to the exit of star man Goncalo Guedes.
Nevertheless, despite the alleged uncertainty, it has been suggested that Gattuso is already eyeing up the first of his transfer targets.
According to Tuttomercatoweb, Gattuso wants to get a deal over the line for Bakayoko, who will be free to leave Chelsea this summer.
The well-travelled Frenchman has just spent a second period on loan at AC Milan, making a total of five starts and 13 substitute appearances in all competitions.
Bakayoko's priority during 2022-23 will be to play regular first-team football, something which may be achieved if he is reunited with a familiar face.
The 27-year-old featured weekly under Gattuso for Napoli during 2020-21, a total of 44 appearances his most activity since the 2016-17 campaign.
As it stands, Bakayoko is halfway through a two-year loan at Milan, but the newly-crowned Serie A champions would welcome the opportunity to end that agreement 12 months earlier than scheduled.
In theory, Chelsea will likely agree to Valencia taking over the agreement on the same conditions, which comes with an option to buy in 2023.
Although Valencia may insist on any permanent fee becoming optional, rather than mandatory, Chelsea's new owners could be open to finding a compromise in order to establish the best deal for all parties.
Bakayoko currently has a contract at Stamford Bridge until 2024 and unlike in the past, Chelsea may opt against further extending those terms with the player having no future under Thomas Tuchel.