Shaw’s Old Trafford career has been plagued by injuries and he has failed to convince Jose Mourinho of his ability.
The 22-year-old has had to settle for appearances coming off the bench, while Daley Blind and Ashley Young have been rotated on the left side of defence.
Meanwhile, United have been keeping an eye on Tottenham star Danny Rose, and they could resurrect their interest in the England international when the window reopens.
Talk of a swap deal involving Rose and Shaw has cropped up, especially with the latter knowing Mauricio Pochettino from their time spent together at Southampton.
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Luke Shaw could leave Manchester United in January
He needs two, three, four, five or six matches in a row to play, to make mistakes, to get condition
And now according to The Gambling Times, at least half a dozen Premier League clubs have expressed an interest in signing Shaw, including Tottenham.
The report says Shaw is considering his World Cup ambitions and believes he has a better chance of making the plane for Russia next summer if he is playing regular football.
It is also said Mourinho will only entertain a move if he can get a replacement.
Mourinho however has refused to shut the door on Shaw’s United future, as he said: “He has a future here but the situation is not easy because he comes from injury after injury after injury.
Mauricio Pochettino could reunite with Luke Shaw
"He needs two, three, four, five or six matches in a row to play, to make mistakes, to get condition, to get match fitness and I cannot give him that.
“If he was a central midfielder then yes, because we only have two but at left back we have so many options. So the situation is not easy.
"But he is in the squad, he works and maybe the opportunity comes.”