The England international went into surgery last week to have metal bolts removed from his leg which were originally inserted after he broke his leg in a Champions League clash in 2015, says the Telegraph.
Interim boss Ralf Rangnick hoped to have Shaw back in a matter of weeks but the operation is taking longer to recover from than initially expected.
It's said the 26-year-old could be set to miss the rest of the campaign in a blow to United's ever-reducing hopes of qualifying for next season's Champions League.
Dropped points in the draw with Leicester and the 1-0 defeat at Everton, have left United seventh in the table - six points off Tottenham who occupy the final Champions League spot.
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