The 24-year-old Brazilian was the subject of a bid from Chelsea back in January while André Villas-Boas was still in charge at Stamford Bridge.
And Spurs have also been linked with a January swoop for the midfielder since the Portuguese coach took over at White Hart Lane.
Willian was in top form as Shakhtar beat Champions League holders Chelsea 2-1 in midweek – and the playmaker is making no secret of his desire to seal a move away from the Donbass Arena.
“I’ve already made it clear to everyone. I want to go, I want to reach new goals,” Willian told the Sun.
“My mission here in Donetsk is accomplished but I have to remain playing at a high level because I need to show up at a big club to be called up for the national team.
“If I were playing in a bigger league the same way as I’ve played here, I would have more chances for Brazil.
“To play in the World Cup in Brazil is my dream and it is only going to happen if I move.”
Before Tuesday’s game, Chelsea boss Roberto Di Matteo had revealed that he is a keen admirer of the attacking midfielder after confirming the Blues’ interest in him earlier in the year.
“As an assistant [at the time] I wasn’t involved in those conversations but Willian is a fantastic player with good qualities,” said Di Matteo.
“We have a good squad with good players and I don’t know where his future is, but the way he is playing here he looks quite happy.”
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