The 22-year-old has been in fine form and played a key role in the centre of the pitch to help his side win the Ligue 1 title for the first time since 2000. In addition to this, he helped his side make it to the semi-final of the Champions League, which they lost to Juventus.
Bakayoko's form for Monaco has seen him attract interest from the Premier League clubs. According to the Daily Mail, the Red Devils and the Merseyside club, along with PSG have all approached the French international via his representatives.
However, it is the Premier League champions Chelsea who are leading the race for his signature. The Blues have tabled a £40m ($52m) bid for Bakayoko and a switch to Stamford Bridge remains a priority for the player.
The Telegraph reports that the Monaco star remains Chelsea manager Antonio Conte's key summer transfer target. Bakayoko is open to the idea of making a move to the English capital and if he fails to agree a deal with the west London club, he will then opt for a move to United.
Should Bakayoko join Chelsea, there will be concern over Nemanja Matic's long-term future at the club. The 28-year-old Serbian international is also wanted by the Red Devils as Jose Mourinho is targeting a reunion with his former midfielder at Old Trafford, according to the Manchester Evening News.
United's primary target was Tottenham Hotspur's Eric Dier. However, the 20-time English champions are of the belief that it will be difficult for them to negotiate with Spurs chairman Daniel Levy in order to sign the English midfielder.
Bakayoko has 46 appearances to his name across all competitions for Monaco this season, scoring three goals and registering an assist in the process.