The Red Devils have been chasing both Sergio Ramos and Nicolas Otamendi for much of the summer, but with the former close to penning a new deal at Real Madrid and the latter thought to be a target for Manchester City, it appears that Louis van Gaal is looking elsewhere.
Chelsea have already had three offers rebuffed by Everton for Stones, with the Merseysiders reluctant to sell their impressive 21-year-old.
However, reports claim United are hopeful of swooping late in the window to beat their rivals to the youngster.
The Premier League giants are even ready to offer Jonny Evans in exchange in the hope that Everton are tempted by the chance to land a direct replacement.
United’s chances could also be boosted by the increasing hostility between the Merseyside club and Chelsea, with Stamford Bridge players such as Gary Cahill having publically urged Stones to leave Goodison Park.