The Blues stepped up their interest in the Brazilian on Monday, but saw their £16.6 million bid rebuffed by the Ukrainian giants.
Club CEO Sergei Palkin has urged the West London side to up their offer for the 23-year-old, who was been linked with Arsenal in the past.
And while the flamboyant midfielder has a release clause of around £29m in his contract, it is believed anything above £20m will convince Shakhtar to part with the player.
Willian has admitted he has his heart set on a move to England,saying: "I wouldn't have any fears about coming to England because I have played against English sides in the Champions League and studied the English game.
"To play in a league that is seen throughout the world would be good for my hopes of playing regularly for Brazil, especially with the World Cup at home in two years' time.
"That is my aim. I've worked hard for four years to establish myself in the national team.
"It has taken that long but now I feel I have a good relationship with the coach and I want to keep working hard, so I remain in the side.
He added: "There are times when you look at your life and realise how lucky you've been.
"I've played for a great club in Corinthians and been successful. I moved to Shakhtar and that turned into a great move too.
"There was talk about Barcelona and Arsenal but now Chelsea are interested.
"If the next step of the adventure is England, then I would be excited by that."
Andre Villas-Boas' side are expected to return with an improved bid before the close of the transfer window next week.
By Ben McAleer
