The Brazilian was left disappointed after Shakhtar were reported to have rejected bids from both London clubs during the summer transfer window.
Andre Villas-Boas, the Tottenham manager, had a £16.7m (Dh98.2m) bid for Willian knocked back in January while at Chelsea, and was linked with another move during the summer.
Willian, who revealed he remains in touch with seemed to pave the way for a move in January after admitting he would still be keen on a switch to London.
"There were two offers in the summer," he told Lancenet.
"One from Chelsea and one from Tottenham. Choosing between the two clubs would be difficult. I don't know."
"Tottenham is a big club and it has a good person in charge. Andre Villas-Boas wanted to bring me to Chelsea and also tried at Tottenham.
"He always sends me messages. We are always in touch, and he has become a friend, for sure. And Chelsea is Chelsea. They are a great team, with amazing players and are the champions of Europe."
Willian, who is expected to start Shakhtar's Champions League match against Chelsea tomorrow night, added: "I would love to play for either of those clubs. But my mind remains at Shakhtar, and I'll do my best to get the win against Chelsea.
"Everybody knows what my goal is. I've clearly stated that I would like to play in a bigger stage, whether it be England, Spain or Italy.
"I want to come back to the national team, and being in a bigger spotlight would help me get noticed."