The Monaco midfielder is one of the most sought after players in Europe after an impressive season for the Ligue 1 table toppers.
The 22-year-old was also pivotal as they caused a Champions League shock by knocking Manchester City out of the competition earlier this month.
Manchester United transfers: Most likely summer deals
Tue, March 28, 2017
Express Sport brings you the most likely Manchester United summer deals according to Betfair
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John Terry – 100/1
Chelsea have been heavily linked, with reports suggesting a deal had already been agreed.
But according to the Manchester Evening News, United are also interested.
Monaco midfielder Tiemoue Bakayoko
However they must have Champions League football to get him.
The report quotes a source close to Bakayoko saying: "Tiemoue is listening to some clubs from England, including Manchester United, but there is nothing concrete right now.
"Manchester United is a big club and [Jose] Mourinho is a big coach, and Tiemoue needs a big coach to continue his progression.
Jose Mourinho will spend big in the summer
"He wants to play in the Champions League and it will be a worry for a club that does not play in it. It will inevitably be taken into account."
United are currently fifth in the Premier League table, four points off a qualification place for the Champions League.
Mourinho's side could guarantee a place in next season's competition if they win the Europa League and they face Anderlecht in the quarter-finals.