The former France Under-21 international was part of the Ligue 1 title-winning side at Montpellier in 2011-12, having come through the club's youth system.
However, he now looks set to leave for Spurs, having featured regularly for the French club in recent seasons.
Montpellier tweeted: "An agreement has been reached between Montpellier and Spurs for the transfer of Benjamin Stambouli."
Making 37 league appearances last term and scoring twice, Stambouli was a rare bright spot in a disappointing campaign that saw Rolland Courbis' men finish 15th.
The 24-year-old then caught the eye of several clubs around the continent, with the likes of Fiorentina, Marseille and Swansea City all linked with a move for the player.
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