Centre back Senesi was a key part of the Bournemouth side that achieved European qualification this season, but the Argentine turned down three contract offers from the Cherries to remain in Dorset.
He had begun talks in January with major European clubs, but Senesi now looks set to join Spurs, according to the BBC, with personal terms yet to be finalised but the move is progressing towards completion.
Tottenham had a poor season in the Premier League and only confirmed their survival on the final day, while Bournemouth finished sixth and qualified for the Europa League.
Senesi remained committed to the Cherries and played all but one of the club's league games, with that absence down to suspension.
He provided five assists from centre back - the most from a player in his position in the league.