A statement on the club's website says a deal is in place for the deep-lying playmaker, previously linked with Swansea, who underwent a medical at Spurs on Friday night.
The announcement read: "MHSC and Tottenham Hotspur FC have reached an agreement regarding the transfer of Benjamin Stambouli.
"He should go to London in the next few hours to undergo a medical and finalise his contract."
Tottenham have so far declined to comment on the announcement, but should the deal go through the 24-year-old will become new boss Mauricio Pochettino's sixth signing of the summer.
Defenders Ben Davies, Eric Dier, DeAndre Yedlin and Federico Fazio have all arrived since Pochettino succeeded Tim Sherwood at the end of last season, while has also signed goalkeeper Michel Vorm.
Tottenham have also bid for Southampton midfielder Morgan Schneiderlin, but the Argentine's old club refused to sell and Sky sources understand a deal is unlikely before the end of the window.
Spurs are also in talks to sign Manchester United forward Danny Welbeck on loan but face competition from Arsenal.