Bakayoko looked destined to become a Chelsea player this summer after Antonio Conte identified him as his top target to replace Nemanja Matic.
Bakayoko appeared all set to join Chelsea - with Matic going to Old Trafford - but the move was suspiciously slow in finalising.
And according to the Daily Star, Jose Mourinho has now swooped to beat Conte to another signing after landing Romelu Lukaku.
Lukaku also looked set for Chelsea before United came in at the last minute and beat them with a £75m offer.
The Everton striker has now clinched his move to the Red Devils and Bakayoko could follow suit.
Bakayoko was a key part of the Monaco team that beat Paris Saint-Germain to the Ligue 1 title last season and reached the semi-finals of the Champions League.
He made 46 appearances for Leonardo Jardim’s side, earning himself full senior honours for France in March.
It would be a double blow for Conte should Mourinho land the 22-year-old, as his arrival would scupper any deal for Matic, who the Blues boss is ready to ditch.
Bakayoko and Chelsea never agreed on personal terms but United have shown they won’t make money an issue after landing Lukaku by paying big bucks to his agent Mino Raiola.
And the 24-year-old Belgium striker rubbed salt into Chelsea’s wounds by claiming he had joined the "biggest team in the world" in Manchester United.
“This is an opportunity that I’ve always wanted since I was a child,” said Lukaku.
“When [Manchester United] came calling, I didn’t have to think twice. So I’m really delighted to hopefully be part of their history.
“Who would say no to the biggest club in the world? Best stadium in England, the best fans.
"This is the perfect opportunity. I always said I wanted to play for a team that’s challenging for every trophy that there is.
“Manchester United at the minute wants to be the dominant team, that dominant force. If you look at their history, it says enough.”
Source: Daily Express