The Brazil international has shone for the Ukrainian side since joining from Corinthians in 2007, and his form has now attracted the attention of the European champions.
Shakhtar president Rinat Akhmetov has been quoted as saying Willian is available for £23.5million, while coach Mircea Lucescu claimed Chelsea have recently seen a £25.5million offer rejected.
"I don't know what the coach said, but the correct value is 25million euros (£19.5million)," Willian told Globo Esporte.
"Regardless of the price, it is clear that the desire is great to play at a club like Chelsea, the champion of the Champions League.
"I'm really upset with the board for not letting me leave. It would be good for me and also for the club.
"I'd be in a big city and have the chance to grow professionally. This is not a message to anyone, everyone knows I want to leave."