That’s according to beIN SPORT journalist Tancredi Palmeri, who says Chelsea have put £21.3m bid on the table.
He tweeted: “Antonio Conte has personally talked with Atalanta’s manager on Kessie, announcing [to] him the €25m (£21.3m) bid.”
Kessie is in demand with Jose Mourinho also said to be a big admierer.
“Conte has personally talked with Atalanta’s manager on Kessie”
The Ivory Coast international is in demand after taking Serie A by storm this term.
He’s scored six goals and set up two for the Italian top flight’s sixth-placed team.
Manchester United boss Mourinho is said to have called the 20-year-old to congratulate him on his performances so far.
Kessie’s agent George Atangana has claimed all the big sides in the Premier League are keen on the talent.
He said: “We have a lot of interest from the Premier League. Chelsea, Liverpool, Manchester United, Manchester City and Arsenal.
“I cannot say at this stage how much he will cost but we are talking about one of the best young players in the world.
“But for us the most important thing is that the technical project is the right one for him.
“Franck is very, young so we have to be very careful about his development.”