The 24-year-old attacking midfielder completed a big-money move from Shakhtar Donetsk to Anzhi Makhachkala last month, having been heavily linked with a move to the Premier League for much of the transfer window.
Chelsea owner Roman Abramovich had been credited with an interest in adding to his growing South American contingent at Stamford Bridge by luring Willian to west London, with the Blues rumours first circulating under the former stewardship of Andre Villas-Boas.
The Portuguese boss - now in charge at London rivals Tottenham - is believed to be a huge admirer of the forward, and also expressed a desire to bring him to White Hart Lane, in a bid to strengthen his Spurs squad.
However, Willian's decision to make the shorter move from Ukraine to Russia means the Premier League missed out on a top class player, with former Shakhtar team-mate Eduardo saying he is just behind Lionel Messi and Cristiano Ronaldo in terms of talent.
"Willian for me, at the moment, because I know him from training, is in the top five players in the world after Messi and Ronaldo," he said.