The 22-year-old French midfielder was one of the lesser heralded, yet nonetheless most important components of their sensational run to the Champions League semi-finals this past season.
Jose Mourinho is gearing-up for a busy few months and he's in the market for a long-term replacement for Michael Carrick - who turns 36 next month - and Bakayoko was among the United bosses targets.
A deal worth 40 million Euro plus bonuses has been agreed, with many suggesting that the transfer could be announced as early as tomorrow if personal terms were agreeable between both sides.
Former Blues assistant coach Ray Wilkins has said how he was "disappointed" to see that Conte was after Bakayoko.
He was also part of the best central midfield partnership in the league this past season (alongside the Player of the Year, N'Golo Kante) and has now amassed 146 appearances for the Blues in his second stint at the club.More news: Japan approves contentious bill against planning crimes
He joined Monaco from Rennes in 2014 and has improved year-on-year as a defensive midfielder.
Bakayoko earned his first France cap in March after coming on for Adrien Rabiot during a 2-0 defeat to Spain.
Not to forget, he scored the decisive goal to knock Manchester City out of the Champions League.
The Serbian worldwide has played an integral part of the Chelsea team as a combative defensive midfielder ever since returning to the club from Benfica in 2014, winning two Premier League medals and a League Cup. Overall, last season, Tiemoue featured in 51 games for Monaco, scored 3 goals and also provided an assist.