Reports suggest United have made a bid of around £16 million for the 24-year-old Argentina international and that Rojo has refused to train with Sporting, handed in a transfer request and asked to be allowed to join the Red Devils.
Sporting president Bruno de Carvalho has been quoted as saying that both Rojo and team-mate Islam Slimani are "subject to strong disciplinary measures" and will not play in the club's Portuguese league opener against Academica on Saturday.
De Carvalho, quoted by Portuguese newspaper Record from an interview with Sporting TV, said: "They will not play next weekend.
"This will take as long as it takes. If something doesn't change, you're going to end up with the players seeing out their contracts.
"They can watch the game on television.
"On Saturday, against Academica, we will play to win and we will win.
"There is no player bigger than the club. I would not give up the honour, the club's history, for the attitudes of anyone.
"I give a piece of advice: don't use the press, be professional.
"These two, in defence of our magnificent group, must be removed. They are subject to strong disciplinary measures.
"Both players have taken decisions that have caused sharp indiscipline at Sporting.
"A message: any player who does not follow the rules of the club can have illusions and pretensions, but with the way these two did things, the situation is just complicated."
- Sports & Recreation