The Nerazzurri have enjoyed success in transfers from the Premier League, having landed Romelu Lukaku and Ashley Young from Manchester United in addition to Eriksen.
According to Corriere dello Sport, coach Antonio Conte is keen to bring Belgium international Vertonghen to the Stadio Giuseppe Meazza this summer and work has already begun on convincing the former Ajax man to make the switch to Serie A.
With his contract set to expire at the end of the season, Vertonghen will be a free agent and looks set to leave Spurs after eight seasons in North London. Conte has identified the 32-year-old as a potential replacement for Diego Godin in his preferred three-man defence, alongside Milan Skriniar and Stefan De Vrijs.
Vertonghen has scored 11 goals in 308 appearances for Spurs and helped the club to the Champions League Final last term, ultimately losing out to Liverpool.