The 18-year-old full-back – a shock inclusion in England’s World Cup squad – has been the Red Devils’ main target for some time as they plot to replace veteran Frenchman Patrice Evra.
Although Chelsea were rumoured to be leading the race, United’s willingness to match the Saints’ £30m valuation has seen them move into pole position.
Shaw himself is thought to have been swayed by the chance of joining one of the country’s biggest club sides, with first-team guarantees believed to have been a major factor.
The main doubt with the deal had been the Old Trafford side’s management situation, but with Louis van Gaal’s arrival having been confirmed the path looks clear for Shaw to sign.
The teenager is likely to be one of a number of high profile arrivals at United, with LVG set to spend in the region of £150m to rebuild the 2013/14 champions’ ailing squad on the back of a disastrous campaign.