The deal is yet to be officially announced, but Bakayoko, who joined the Blues from Monaco earlier this summer, does not fear for his place.
"Danny Drinkwater doesn't scare me," the Frenchman told SFR Sport. "It's the competition. It's good, I think every team needs that. It makes you improve."
Chelsea are believed to be keen to strengthen their midfield following the departure of Nemanja Matic to Manchester United.