The former Spurs manager recently took charge of the Russian giants, and is expected to be backed heavily by the Gazprom-funded club in the transfer market.
A top class centre-back is said to be on his agenda, with the unsettled Belgian a top target.
Vertonghen has been agitating for a move away from White Hart Lane in search of Champions League football in recent times, with his on-field appearances backing up claims that he has grown disillusioned in north London.
AVB brought the silky defender to Tottenham from Ajax in 2012, and is keen to reunite with him this summer.
Although Vertonghen is said to enjoy life in the Premier League, Zenit could be an appealing option due to the lucrative salaries offered by the club and the virtual guarantee of top level European action.
Manchester United may benefit if the move goes through.
Should the Spurs ace switch to the Petrovsky Stadium, the Red Devils could find themselves unopposed in the race for Benfica defender Ezequiel Garay – another rumoured target for Villas-Boas.