The Tottenham boss revealed his club has held talks over the Brazil international, and also quashed suggestions Gareth Bale has already agreed to join Real Madrid.
Willian is one of a number of stars set to leave Anzhi, and Spurs have made the 25-year-old a prime target as they pursue a €70 million swoop for the Brazilian and Roma forward Eric Lamela.
"I can't really confirm anything regarding Willian," Villas-Boas told reporters. "There is interest in the player and there have been conversations. None of the names you have mentioned have signed for Spurs. I have answered about Willian in the past - not only time with Tottenham but also Chelsea.
"All the players are great, great players. On the players that are here, we are moving forward. We are not only trimming the squad but adding tremendous talent.
"I think we can become very, very strong regards to last season. It depends what deals we are able to conclude before the end of the market. We are looking to be stronger than before."
But the Spurs boss moved to deny reports that Gareth Bale has already agreed a deal to join Real Madrid, with the two clubs still at loggerheads over a fee for the Welshman.
"I cannot say anything about that but it is not true," he said when asked if a transfer was in place.
Tottenham has been uncharacteristically decisive in this summer's transfer market, moving to sign Brazil international Paulinho and Valencia striker Roberto Soldado with weeks of the transfer window to spare.
Technical director Franco Baldini has been credited for affecting this change in approach, and Villas-Boas is full of praise for the Italian.
"Franco is a massive appointment for Tottenham," he continued. "He's someone I wanted last year and it wasn't possible then. He has massive experience with Real Madrid, Roma and the FA. He is one of the best technical directors there is."