The full-back, who is currently on £100,000-a-week, will become one of the world's top earning defenders.
It is understood Man United's top brass have been in discussions with the 23-year-old for several weeks and are hoping the new deal can be concluded swiftly.
Shaw has been a shining light in an otherwise dire season for Jose Mourinho's side.
The England international has finally replaced Ashley Young on the left-flank in the team, featuring in seven out of eight Premier League fixtures for the Red Devils.
He also recorded his first goal for the club in their opening league fixture against Leicester.
But it has not always been plain sailing for the former Saints player – who signed for Man Utd for a fee of £30million in 2014.
He has struggled with injury and has also had a fractious relationship with Jose Mourinho.
The Portuguese made several attacks on the full-back last season, including when he furiously took him off at half-time in their FA cup victory over Brighton.
However, Shaw was determined to fight for his place in the Special One's side and has made an assured comeback for the team this season.
Shaw's performances also merited an international recall by England Gareth Southgate.
He hasn't been in the current England squad due to injury but is aiming to be fit again when Manchester United face Chelsea on Saturday in the early-kick off when the Premier League returns.
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