The Chile international is fighting to regain fitness after suffering a hamstring injury at the back end of the Copa América, where Sánchezs two-time defending champions suffered a shock defeat in the semi-finals to Peru.
Upon returning to Manchester United, Sánchez has been desperately trying to regain his fitness and fight his way into manager Ole Gunnar Solskjaers first-team ahead of the 2019/20 season.
And it was in one of his first training sessions back that The Sun claims Sánchez clashed with 17-year-old Greenwood following a tackle from the academy graduate, which apparently sparked an angry war of words between the pair.
While its unknown just how severe the falling out was between Sánchez and Greenwood, its apparent that Solskjaer is favouring including the teenage forward following his substitute appearance against Chelsea on Sunday.
The Manchester United manager has, however, spoken highly about Sánchezs chances this season and expects the Chile international to make his mark at Old Trafford, even though the club were recently holding talks to send him to Roma on a season-long loan.
If there is any truth to reports that Sánchez has fallen out with Uniteds most exciting academy prospect then that could see an end to his time at the club, especially as they appear to be building a youth-centred philosophy under Solskjaer.
It emerged on Tuesday that midfielder James Garner, who made his senior debut against Crystal Palace last season, has also been promised playing time in the first team as United continue to build for the future.