The 21-year-old has had a difficult time at Old Trafford since arriving in 2014 from Southampton for £27million.
After sitting out the majority of last season with a broken leg, the England international has found game time hard to come by.
Jose Mourinho has questioned his attitude and commitment to play through pain, but United are ready to persevere and give him a chance.
Luke Shaw is reportedly on wages of £70,000 a week at Manchester United
However, according to the Daily Mail, staff at the club fear Shaw has experienced too much at a young age.
And it is said at one stage this term Manchester United believed he may never realise his true potential.
Matteo Darmian, Daley Blind and Marcos Rojo have been used at left-back, even when Shaw has been available.
Luke Shaw is in full training at Manchester United but can't get in Jose Mourinho's team
Twitter reacts as Man United increase interest in Antoine Griezmann
Wed, January 18, 2017
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Manchester United fans react as Antoine Griezmann is linked with Old Trafford move
Manchester United are very happy with him and he’s very happy at Manchester United
Luke Shaw's agent
Mourinho outlined his decision to leave the ex-Saints man out of his squad to face Liverpool on Sunday was tactical.
But the boss is more concerned by Shaw’s willingness to listen and improve.
A transfer away has been mooted with United targeting Celtic’s Kieran Tierney as a potential long-term solution on the left of their defence.
Although Shaw’s agent Jonathan Barnett has quashed rumours of unrest this week, saying: “He is happy at the club. Manchester United are very happy with him and he’s very happy at Manchester United.”