The Stamford Bridge club have made their move after London rivals Tottenham held talks with Willian earlier on Thursday.
Spurs were ready to splash £30m on the midfielder, who has been offered a five-year contract at White Hart Lane.
But the 25-year-old, who was also linked with Liverpool earlier in the summer, appears to be keeping his options open.
Chelsea have already been busy in the summer transfer window with forward Andre Schurrle arriving from Bayer Leverkusen for £18m.
The Blues also splashed around £8m on Marco van Ginkel from Vitesse Arnhem, and £3m on fellow midfielder Cristian Cuevas.
Spurs boss Andre Villas-Boas says he knows nothing of Chelsea's apparent interest.
Speaking after Spurs' 5-0 win at Dinamo Tbilisi in the Europa League qualifying tie, Villas-Boas said: "We were just involved in a game so unfortunately I can't give you further information.
"I confirmed our interest in the player. Everything is possible, but I'm not aware of the circumstances because of our involvement in the (Dinamo) game.
"I don't want it to be a distraction over what we achieved here tonight."
Meanwhile, Villas-Boas refused to discuss the future of Gareth Bale, with the Wales international apparently about to join Real Madrid in the next 24 hours.
Villas-Boas said: "On Gareth, I am not able to comment on anything that has been my tone since the start of the season and I will not come out of it."