The 24-year-old old missed training last week in a bid to force through a move away from the Portuguese outfit, but he has since admitted that he made a mistake.
"It was all a misunderstanding, I was a hothead. I'm sorry for what happened because I feel that I was unprofessional," Rojo told the club's official TV station.
"My career depends on Sporting. Now I will try to correct the situation. At the time Sporting signed me, it was not a good time I can only thank Sporting."
Manchester United have been heavily linked with a move for Rojo in recent weeks.