The Red Devils are keeping a close eye on the 18-year-old’s development at Goodison Park under Carlo Ancelotti this term.
The report adds that Branthwaite has impressed Ancelotti during his loan spell at Championship side Blackburn Rovers in the ongoing campaign.
The 20-time English champions have also identified the centre-back as a promising defensive prospect during his time at Rovers.
Branthwaite moved to the Toffees in a £1m deal from Carlisle United in 2020.
Man United could face fierce competition from Liverpool and Manchester City for the signature of Branthwaite, who has a deal at Everton until the summer of 2022.