Fosu-Mensah impressed last season after being handed his United debut by Louis van Gaal against Arsenal in February, and went on to make 10 appearances.
And the Daily Mail claim the Dutchman has now he has now agreed a new deal with United.
The report says Jose Mourinho wanted to tie down the 18-year-old’s future to underline his commitment to the club's tradition of developing young players.
Mourinho has spent around £150million this summer on Paul Pogba, Eric Bailly, Zlatan Ibrahimovic and Henrikh Mkhitaryan.
GETTY
Jose Mourinho is being forced to sell before buying any new players
The United boss still wants to bring a commanding centre back to Old Trafford to add experience to his back four.
But ESPN claim the former Chelsea boss has been told the club will have to sell players first before they can make any more signings.
And finally Mourinho has received an apology after being accused of bullying Bastian Schweinsteiger.
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
Dejan Stefanovic, a member of worldwide players’ union Fifpro, accused Mourinho of intimidating the German midfielder, who is free to leave United this month.
But Stefanovic has now spoken to Mourinho to apologise for his outburst.
The League Managers' Association said the comments were "totally inappropriate". It added Stefanovic "has apologised to Mr Mourinho".