The Brazilian attacker arrived in London on Tuesday and has undergone a medical at Spurs but is believed to be considering other offers.
José Mourinho, perhaps mindful of the losing battle he is fighting to bring Wayne Rooney to Chelsea, has identified Willian as an alternative target.
Mourinho claimed earlier this summer Rooney was his only remaining transfer target, but admitted earlier this week he had a "Plan B and Plan C". Villas-Boas was not aware one of the alternatives was Willian, though.
"We were just involved in a game so unfortunately I can't give you further information," the Tottenham manager said.
"I confirmed our interest in the player. Everything is possible, but I'm not aware of the circumstances because of our involvement in the (Dinamo) game. I don't want it to be a distraction over what we achieved here."
Spurs thrashed Dinamo Tbilisi 5-0 in their Europa League playoff win ahead of Gareth Bale's world record transfer to Real Madrid on Friday.
Spurs director of football Franco Baldini held discussions with the nine-time European champions in Madrid on Thursday with a view to concluding the £93 million deal.
It was reported last week Madrid had already pre-ordered 50,000 "Bale 11" shirts, and the Spaniards seem so confident they appear to already be stocking replica shirts bearing the Tottenham forward's name.
The Spanish giants kept the number 11 free when they announced their squad numbers in pre-season and screen grabs of the club's official online shop appeared to show the option to buy a Bale replica shirt for €73 (£62).