The Manchester Evening News claims that Bakayoko is interested in moving to Old Trafford if Jose Mourinho can steer the Red Devils into the Champions League in time for next season.
Bakayoko has made 26 appearances for Monaco this season and has taken the Ligue 1 by storm.
According to France Football, Arsenal coach Arsene Wenger met Bakayoko in a Paris hotel past year to discuss a potential move to London, but it is now Premier League rivals Chelsea who lead the chase.
"Tiemoue is listening to some clubs from England, including Manchester United, but there is nothing concrete right now", a source close to the player told M.E.N Sport.
Chelsea fans are convincing themselves that the club are working on a deal to sign Monaco midfielder Tiemoue Bakayoko this summer.
Ricciardo misses grid at Aussie GP after stopping in warmup
The Australian got into the top ten but failed to set a time in Q3, instead mangling his vehicle in front of the home crowd. One count showed there were just five passes during the Australian Grand Prix , down from two dozen in 2016.
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.
The tweet from Martial only furthered speculation linking Bakayoko with United.
Jose Mourinho's United now sit in fifth place in the Premier League and have failed to qualify for two of the last three competitions. 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.
"It adds to the CV so I think we've got a good opportunity".