Shaw's future has been the subject of intense speculation in recent days after he was hauled off at half time of his side's 2-0 win over Brighton & Hove Albion on Saturday - the latest in a long line of public humiliations at the hands of manager Jose Mourinho.
The 22-year-old is understood to have seen that substitution as the final straw and will now leave Old Trafford in the summer, unless Mourinho goes first.
The Daily Mail reports that Chelsea are among a number of clubs interested in the unhappy England international, having been beaten to his signature by United when he initially left Southampton for £31m in 2014.
Chelsea are likely to face stiff opposition for Shaw with the likes of Manchester City, Arsenal, Tottenham Hotspur and Everton having also been credited with an interest, but the defender grew up as a Chelsea fan which could give the West Londoners an edge.
Shaw has made just 12 starts for Manchester United across all competitions this season and has not completed the full 90 minutes for more than a month.