The Sun says Sanchez, 30, was fouled in one of his first sessions after returning from the Copa America with a hamstring injury.
Angry words were exchanged between the pair as Ole Gunnar Solskjaer's men prepared for the new campaign.
And separately the Chile star also spent time working AWAY from the squad in his bid to return to action and play a part in United's campaign.
Solskjaer insists Sanchez IS part of his plans despite his dips in form since arriving from Arsenal and his determination to bring young talent through.
Greenwood, 17, came off the bench for United at the weekend in their 4-0 win over Chelsea and is set to spend the season around the first-team squad.