Canadian outlet CTV, as quoted by the Daily Express, is claiming that the Red Devils want the 17-year-old to train with them in the new year so they can assess his potential first hand.
The same report claims that the move, however, is dependant on it being given the green light by his club Vancouver.
Davies became the youngest player to score in the United Soccer League as a 15-year-old and then moved to MLS side Vancouver Whitecaps.
Earlier this year, Davies earned his first call-up to the Canadian national team and became their youngest ever goal-scorer when he netted in the CONCACAF Gold Cup.
Manchester United are bound to be linked with a host of players in the coming weeks as the January transfer window draws nearer – but it remains to be seen whether Davies will be allowed to train with the Red Devils in the new year.
The Red Devils are now preparing to return to Premier League action as they gear up for their home clash against Bournemouth at Old Trafford on Wednesday night.
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