The deal for the Frenchman is reportedly worth £52 million, as per Sky Sports.
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It comes as talks continue between Chelsea and Manchester City for Enzo Fernandez, who could move to the sky blues on deadline day.
The 25-year-old is a midfield mainstay for Roma, having made 65 appearances in three seasons in Serie A.
While Kone could be on the way to Stamford Bridge, Jamie Gittens could move the other way in a loan deal to the Stadio Olimpico.