The 24-year-old Argentina international was disciplined by the Portuguese club last week amid reports he missed training in a bid to force a transfer to Premier League giants United.
However, Rojo explained on Sunday that he will go back to training this coming week, adding that he has settled any differences with the Lisbon club.
"It was all a misunderstanding, I was a hothead. I'm sorry for what happened because I feel that I was unprofessional," he told Sporting'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."
Rojo, who impressed for Argentina at the World Cup, has been a regular feature for Sporting since joining from Spartak Moscow in 2012.
However, he was not selected by coach Marco Silva for the club's 1-1 draw with Academica on Saturday on the first weekend of the Primeira Liga.
