The Sunday Mirror says United are already resigned to losing the services of first-choice goalkeeper David de Gea and striker Javier Hernandez, wanted by Spain and Mexico respectively, for the tournament.
The da Silva twins, Rafael and Fabio, could be called up by Brazil while five more United youngsters have been lined up for a summer Under-19s event.
But it is the prospect of losing some of his key British senior players until a week before the start of the new Premier League campaign that has staggered Ferguson.
A dismayed Ferguson said: "It's absolute chaos. It's ridiculous for our pre-season preparations. There are so many competitions on this summer. There are the European Championship, you've got England Under-19s in a tournament and we've 10 players nominated by Britain for the Olympics.
"And it will affect us for the start of the season, as well as pre-season. We have no say in this. There's nothing we can do about it. It's up to the player himself to decide."