The Belgian, who turned 27 last week, has been linked with a move away from White Hart Lane for some time, with rumours having been circulating since Christmas time that he is ready to quit the club.
Vertonghen is believed to be upset that Spurs will once again be out of the Champions League next season, and is considering leaving in a bid to realise his ambition of playing top level European football.
Inter are unlikely to be able to match his desires just yet, but following their recent takeover they are set for a big summer of transfer activity and have lofty plans.
The San Siro side have already tied up Nemanja Vidic’s arrival when his Manchester United contract ends, and are looking at Fernando Torres and Edin Dzeko of Chelsea and Manchester City respectively.
Barcelona and Roma have also been linked with the silky defender, as have domestic rivals Man City.
Vertonghen is expected to play at the World Cup later this year, and may make a final decision on his future after the tournament.