Spurs are well and truly in a fight to keep their Premier League status, sitting in 18th, two points off West Ham in 17th.
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According to David Ornstein, Senesi, who is out of contract at the end of the season, has agreed to join the North London club in the summer.
The deal is conditional, however, and the 28-year-old will only make the move if Tottenham remain in the Premier League.
Senesi fell down the Bournemouth pecking order last season due to breakout starts Dean Huijsen and Ilya Zabarnyi.
He has since reestablished himself as a key player for Andoni Iraola, starting all 31 of his Premier League appearances so far this season.