Antonio Conte is keen to bolster his squad ahead of their return to the Champions League next season with the midfield being one of the priority areas for the Italian manager.
According to the Mirror, Chelsea have offered a lucrative package to the midfielder to sign for the Blues ahead of other interested suitors. They will also be hard to beat in a bidding war as they are flush with the cash earned from Oscar's £52m move to Chinese Super League during the January transfer window.
Bakayoko is contracted to the French club until the summer of 2019, but has rejected the offer of a new deal. The Principality club will be reluctant to let the midfielder leave, but could be tempted to cash-in rather than sell him for a reduced price once he enters the final year of his contract.
The 22-year-old defensive midfielder has been impressive this season for Monaco making 41 appearances in all competitions. He has played a key role in helping his side return to the top of the French League – three points clear of PSG in second – and make the quarter-finals of the Champions League, which included scoring the winner against Manchester City in the last-16 second-leg.
Bakayoko's impressive performances for the club have seen him being called up to the France national team as a replacement for Paul Pogba, who has been ruled out with injury for at least a fortnight, for their clashes against Luxembourg and Spain. The midfielder chose to play for France only recently as he also had the option of representing Ivory Coast.
"I am extremely happy to be called in selection. I had not yet chosen the national team for which I wanted to play. It was decided earlier and I opted for France. I'm proud of it," Bakayoko told French publication L'equipe.