The 22-year-old — who played a pivotal role in Monaco winning the French title and reaching the Champions League semi-finals last season — will cost the English champions up to 39.7 million pounds (45m euros, $51.2m), according to The Guardian.
The deal is conditional on him passing a medical — Bakayoko underwent keyhole surgery on his knee after the season ended and is likely to miss the Community Shield match with Arsenal and the first three Premier League games.
There had been speculation Manchester United might try and stymie the bid for Bakayoko — who made his senior international debut earlier this year — just as they did with Lukaku, as they broke the record for a deal between British clubs of £75m to prise him away from Everton on Monday.
However, Bakayoko — whom Monaco will make a tidy profit on having signed him from Rennes for £7m in 2014 — had always made clear that Chelsea was his preferred destination.
Bakayoko’s arrival — which Chelsea hope to conclude by the time they leave for Asia for a pre-season tour next Monday — should see Serbian midfielder Nemanja Matic leave for a similar fee to that of the Frenchman.
However, Chelsea are not keen to sell him to the original suitors Manchester United, as relations between the two rivals have cooled considerably since the Lukaku affair.
Bakayoko’s signing — joining veteran Argentinian goalkeeper Willy Caballero and German defender Antonio Rudiger as new recruits — would not be the last for manager Antonio Conte.
The 47-year-old Italian, who along with his coaching staff are yet to sign new contracts offered at the end of last term, is hoping to conclude deals for Juventus’ Alex Sandro and Spanish international striker Alvaro Morata from Real Madrid.
Morata is Italian Conte’s preferred fallback option for Lukaku, having lured him to Juventus in 2014 before leaving to take over as national team coach, and would replace temperamental Spanish striker Diego Costa.
Morata told The Guardian earlier this year that he dreamt of playing under Conte because he was a man who had bet on him and understood him.
Costa, whom Conte told was not part of his plans, is likely to rejoin Atletico Madrid even though he would not be able to play for them until January because of the club’s transfer ban.