The 26-year-old has fallen out-of-favour at White Hart Lane, having started just two of the last five games.
Dembele is ready to leave the Premier League side in order to get regular first-team football ahead of the World Cup in Brazil next summer.
Former Liverpool boss Rafa Benitez is reportedly keen to take the highly-rated midfielder to the Serie A in January.
Napoli face competition from the likes of Newcastle, Aston Villa, Southampton, Cardiff and Swansea in the race to sign the midfielder.
Dembele joined Tottenham for a fee of £15million from Fulham in August 2012.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.