Barcelona have reportedly pinpointed Willian as a potential free transfer ahead of next summer's transfer window.
The Catalan club have expressed interest in the Brazilian playmaker for some time but failed with a bid worth £40m over the summer.
Willian, who joined Chelsea from Shakhtar Donetsk in 2013, has a contract which expires at the end of this season and is unlikely to get a fresh one, with the Blues reluctant to hand out new contracts to players over the age of 30.
According to The Mirror, Valverde remains intent on adding Willian to his attacking options this summer and will move to make a bid once the 31-year-old becomes a free agent.
The Barcelona boss has somewhat freed up his attacking options by securing a loan move away for unwanted forward Philippe Coutinho.
Reports have suggested that the La Liga champions are also willing to dispense with Ousmane Dembele after Valverde ran out of patience with the Frenchman.