The France international has been a top summer target for boss Antonio Conte and reports claim the two clubs and player are now close to reaching an agreement and he will be in England in the next few days to finalise the move.
It is thought the 22-year-old, who impressed when making 51 appearances in all competitions to help Monaco win Ligue 1 and also get to the Champions League semi-finals last season, will join for around £35million.
Bakayoko is set to be the first signing in a busy summer transfer window at Stamford Bridge as Conte looks to strengthen his squad for a return to the Champions League.
Romelu Lukaku is widely expected to join from Everton while Juventus defender Leonardo Bonucci, Everton midfielder Idrissa Gueye and Southampton centre-back Virgil van Dijk are other targets.
Diego Costa, meanwhile, is set to depart after being informed he’s not part of Conte’s plans next term.