The 22-year-old was an integral part of Leonardo Jardim's side that won the league, which was their first title since 2000. The Ligue 1 outfit also made it to the semi-final of the Champions League.
Bakayoko's form has seen him attract interest from the Premier League clubs and the Blues were believed to be leading the race for his signature. The Daily Mail earlier reported that United had outbid their league rivals in signing the France international.
Chelsea have already lost Romelu Lukaku to United after the Everton striker rejected an opportunity to return to Stamford Bridge in order to reunite with Jose Mourinho at his current club.
Sky Sports now claims the Red Devils have not tabled any bid for the Monaco star, despite reports suggesting otherwise. Bakayoko's move to Chelsea is set to go through and the player is expected to undergo his medical this week.
The Blues have already completed two signings so far in the summer transfer window. Manchester City released Willy Caballero after his contract expired and the goalkeeper became Antonio Conte's first signing. Antonio Rudiger was the west London club's second signing as he joined the English club from AS Roma.
Conte wants to complete Bakayoko's signing before the team flies for a pre-season tour of China and Singapore next Monday. The midfielder will cost the Premier League winners around £40m ($51.4m).
His arrival will then see Chelsea sanction Nemanja Matic's sale, who is wanted by United manager Mourinho. The Portuguese tactician is planning to reunite with the Serbian international at Old Trafford. However, the Blues are not willing to allow Matic to join another Premier League side and are planning to sell him to a foreign club this summer.