The 35-year-old also suggested his side were not in the market for Porto's Colombian striker Jackson Martinez this summer
Earlier in June, the 20-year-old's agent, Hissa Moyses, claimed Tottenham were the only side in the running for the player after suggesting Borussia Dortmund were not planning on submitting a bid.
Bernard is currently in Brazil's squad for their Confederations Cup campaign and made his first appearance in the tournament on Saturday after coming on as a second-half substitute for Neymar against Italy.
Villas-Boas also dismissed reports suggesting Tottenham are looking to sign Porto striker Jackson Martinez.
”Jackson Martinez? No. Bernard? He’s a player that we monitor like others, but I think nothing will happen," Villas-Boas told reporters.
On Saturday, Tottenham agreed a £17 million deal with Corinthians for their midfielder Paulinho.
The Brazil international will move to White Hart Lane after the Confederations Cup on a four-year deal, with Tottenham holding the option for a one-year extension.
Tottenham will pay £15m for the 24-year-old with a further £2m in potential add-ons for the powerful midfielder, who has a £17m release clause in his contract.