The 22-year-old has caught the eye for the Ligue 1 side this season, making a particular impression in the Champions League.
And his performances have led to interest from Europe's top clubs.
Manchester United player ratings against Watford
Sat, February 11, 2017
Express Sport brings you our Manchester United player ratings from their clash with Watford at Old Trafford
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How did the Manchester United players rate during their clash with Watford?
Manchester United were keen to sign him in January but Monaco refused to do business.
But United are prepared to make another attempt for Bakayoko at the end of the season.
And according to reports in France, this latest development could pave the way to an exit.
Monaco midfielder Tiemoue Bakayoko
French daily Le Parisien say Bakayoko has rejected an initial contract extension from Monaco.
It is also claimed there is 'tension' between the club and Bakayoko over the contract.
Bakayoko, who made 32 appearances in this season, has a contract at Monaco until 2019.