The Metro report that the Premier League champions-elect have agreed a £35m deal with Monaco to sign Bakayoko this summer with the midfielder set to sign a lucrative five-year contract.
However, in a blow to Chelsea's summer plans, Bakayoko's brother Soualio - who also acts as his agent - has underlined the 22-year-old desire to play for PSG.
But Bakayoko, whose Monaco team beat Manchester City in March to reach the Champions League quarterfinals, reportedly wants to play in the same competition next season.
"Manchester United is a big club and [Jose] Mourinho is a big coach, and Tiemoue needs a big coach to continue his progression".
Monaco - who face Borussia Dortmund in the last eight of the Champions League - lead PSG by three points with eight matches remaining and the clubs meet in the Coupe de la Ligue final on Saturday.
Microsoft to start rolling out Windows 10's Creators Update on April 11
These configuration settings will now be put directly in front of you, so you can actively choose whether to allow them or not. Like the original Microsoft Paint it's a fun showcase for Windows' potential rather than a serious tool in its own right.
According to the Manchester Evening News, Bakayoko wants Jose Mouinrho's side to qualify for the Champions League next season. "It will inevitably be taken into account".
Chelsea target Tiémoué Bakayoko "would like" to play for PSG and "wouldn't hesitate" if they called him, his agent has confirmed. "He's always dreamed of moving there".
"When I asked him to imagine that he'd move to PSG one day, he told me that he'd 'honestly like that". "If I have to go to PSG, I will go, that is all". "They've won the League Cup and are in the Europa League and I think they've got a great chance there".
"But he said, "I have time".