The 32-year-old's contract in North London expires at the end of this season, and talks over an extension have stalled despite both the player and manager Jose Mourinho being keen to agree terms.
Vertonghen has been free to speak to overseas clubs since January having entered the final six months of his contract, and the Evening Standard reports that Inter have already made contact.
The Belgium international has slipped down the pecking order in recent weeks following the emergence of Japhet Tanganga, although he did make his first league start for a month in Saturday's 2-1 defeat at Chelsea.
Inter are understood to view Vertonghen as a possible replacement for Milan Skriniar, who has been linked with a move to Manchester City this summer.
Antonio Conte's side have already signed Christian Eriksen from Spurs for a cut-price £17m fee this year, while they have also brought in Romelu Lukaku, Alexis Sanchez, Ashley Young and Victor Moses from other Premier League clubs this season. body check tags ::