The 25 year old appeared to be on the verge of securing a move to Tottenham Hotspur, but the Blues have moved to hijack the deal with a bid of their own.
Anzhi are attempting to move on a number of their high earners, and Brazil international Willian is one who has generated much interest.
Liverpool had been linked with a move for the winger, though he flew into London to open talks with Spurs earlier in the week.
However, Jose Mourinho has revived his interest in the player as he looks to bring in more new signings before the transfer window closes on September 2nd.
The Chelsea boss is also expected to make a final bid for Manchester United striker Wayne Rooney, but not until after his side travel to Old Trafford to face the Premier League champions on Monday evening.