Reports in Italy have claimed that Spurs are ready to open talks with Silvestri's agents to gauge his interest in a move to White Hart Lane.
The 21-year-old is currently on loan at Padova from parent club Chievo, and has impressed in Serie 'B'.
Villas-Boas has good competition for places at Tottenham. Hugo Lloris displaced Brad Friedel as Spurs number one earlier this season.
But with the 41-year-old American is thought to be keen to play first-team football, and Villas-Boas may look to bring in a younger understudy to Lloris in the summer.
Silvestri is rated as one of the most promising young talents in Italian football, and the 6ft 3in keeper has been capped by Italy under-21s.
Spurs face Inter Milan in the first-leg of their Europa League last-16 tie this evening. Lloris is expected to start for Villas-Boas's side at White Hart Lane, as the club looks to win its first European trophy since its UEFA Cup triumph in 1984.
They come into the match full of confidence following their victory in the north London derby over Arsenal last weekend.
Goals from Gareth Bale and Aaron Lennon proved to be enough to hand Tottenham a 2-1 victory at White Hart Lane, propelling Spurs up to third in the Premier League table.