The 22-year-old, whose contract at Monaco runs until 2019, has played 37 matches for the Ligue 1 leaders and was recently called up for the first time to play for France during the current worldwide break.
The Daily Mail report that Bakayoko has always dreamed of a move to Monaco's rivals Paris Saint-Germain, which may come as a blow to United regardless of their ability to qualify for the Champions League.
Chelsea reportedly have a deal in place with the holding midfielder, worth in the region of £35 million, but it's understood that Bakayoko could yet be swayed to move to Old Trafford. on one condition.
"Tiemoue is listening to some clubs from England, including Manchester United, but there is nothing concrete right now", a source close to Bakayoko told the Manchester Evening News. The French star had already attracted interest from Chelsea and PSG, with word spreading that he has already agreed personal terms with Antonio Conte's side. "He has always dreamed of PSG. If I have to go to PSG I'll go, that's all'".
Join in with great town centre Easter Egg Hunt
Peter Cottontail will be at the library to eat donuts with the children and will be available for pictures. Altrincham town centre is gearing up for a week of free family activities in the run-up to Easter .
"When I said to him, "Imagine, one day, you sign for PSG", he told me, "I would really like that".
Bakayoko has been turning heads with his displays for the principality outfit and Premier League leaders Chelsea are thought to be keen on the 22-year-old.
"But he said, 'I have time".
Bakayoko will join back up with his Monaco team-mates after France face Spain in a glamour friendly on Tuesday night at the Stade de France.