Blues manager Antonio Conte has identified France international Bakayoko as a player who can strengthen the Premier League champions' squad.
Talks have taken place and the transfer - which would be Chelsea's first of the summer - could be completed this week.
Bakayoko, 22, was part of the Monaco squad that reached the Champions League semi-finals last season.
He joined the club from Ligue 1 rivals Rennes in 2014 and made his France debut in a friendly defeat by Spain in March this year.
Juventus and Brazil wing-back Alex Sandro is also thought to be a target for Conte, and the Blues have been linked with re-signing Everton's Belgium striker Romelu Lukaku and Southampton and Netherlands defender Virgil van Dijk, who Liverpool apologised for approaching earlier this month.
In terms of outgoings, Chelsea forward Diego Costa has already revealed a text from Conte informing the Spain international he should find another club.
The future of Dutch defender Nathan Ake is still to be decided, despite reports linking him with a £20m move to Bournemouth.
Chelsea are close to signing midfielder Tiemoue Bakayoko from French champions Monaco.