The Telegraph says Spurs are still reeling from the news that Harry Kane is likely to be out until April with a hamstring injury, leaving them with no fit striker.
But Palace have offered out-of-favour forward Benteke.
Spurs boss Jose Mourinho is understood to be desperate to sign a stand-in striker and the 29-year-old is surplus to requirements at Selhurst Park after the Eagles signed Cenk Tosun on loan from Everton.
Benteke has not scored all season, but his recruitment would mean natural wide player Son Heung-min would not have to play up front in Kane's absence.
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