With Patrice Evra widely expected to leave the club this summer, United are known to be in the market for a new left-back and have wasted little time making an approach for the England star.
Shaw has also been linked with Chelsea, the club he supported growing up in South West London. The Blues are also expected to lose Ashley Cole in the summer.
However, United have moved first, and the prospect of a guaranteed first-team place could sway the 18-year-old, who is expected to be on the plane to Brazil for England's World Cup campaign.
Shaw made his debut for Southampton in November 2012 and made his first appearance for England against Denmark in February.
United have endured a difficult season which saw them finish 7th in the league and are expected to overhaul an aging squad come the summer with Shaw the first of a number of expected arrivals.
- Sports & Recreation