Spurs are looking to land a striker this summer and have outlined the Belgium international as one of their top targets.
They are prepared to offer Emmanuel Adebayor as a makeweight in the deal along with £20m.
A source told the Daily Star: "Benteke is one of the players they want. Sadly, no one has come in for Adebayor so at the moment so it must be straight cash."
Benteke had an outstanding first season in the Premier League for Aston Villa, scoring 19 goals.