Nemanja Matic along with Cesc Fabregas face uncertain futures at Stamford Bridge.
Reports earlier this week suggested the Blues are hoping to complete a double deal for Bakayoko and Romelu Lukaku, who has refused to commit to a new deal with Everton.
And it seems a move for Bakayoko is on the cards.
Tiuemoue Bakayoko could head to Chelsea
The Daily Mail claim the 22-year-old is edging closer to a deal that could see the Blues shell out £35million for the Monaco star.
The report says should Bakayoko join, it would tempt Conte to listen to offers for Matic.
Manchester United are eyeing a deal and Matic, it is suggested, would be keen on reuniting with Jose Mourinho at Old Trafford.