Sky Sports News says an agreement is all in place for the Anzhi Makhachkala man who will join for a reported fee of £30 million with the player telling the channel he will finish his medical on Thursday.
"I can't really confirm anything regarding Willian. There is interest in the player and there have been conversations," Villas-Boas said at a press conference prior to Tottenham's Europa League play-off against Dinamo Tbilisi.
Villas-Boas declared his appreciation for Willian on Monday and he has moved quickly in his attempts to sign the player following interest from Liverpool.
Should Willian pass his medical and sign for Tottenham, for a fee of around £30million, the north London club will break their transfer record for a third time this summer.
Spurs have already spent £60million on new players this summer, but their manager hopes to strengthen his squad further.
"We will see some new players in defence and attack," Villas-Boas said.
"They have not signed for Spurs. Both of them are great, great players, but I cannot extend myself," he said.