The Sporting Lisbon defender has just returned to training with the Portuguese giants after apologising to them for previously refusing to play, as he looked to force through a transfer out of the club.
Both United and Southampton had lodged bids for the 24-year-old, but it is United who are set to win his signature - although neither club has yet confirmed whether a deal has been agreed.
It is understood talks are continuing between United and Sporting, with reports claiming that Nani and Anderson could be loaned the other way as part of the deal.
But one thing that is sure, is that Rojo - who has won 28 caps for Argentina - believes he will be at Old Trafford sooner rather than later.
"It's a dream to play at Manchester United and I am very proud of having the chance of working with [Louis] van Gaal," Rojo said in an interview with Argentinian radio station Continental.
Rojo, who can play at left-back or centre-back, has revealed that he always wanted to play for United, after speaking with former United midfielder Juan Sebastian Veron earlier in his career.
"I spoke with Juan Sebastian Veron about Manchester United when we were at Estudiantes," he said.
"I have always liked English football, and I should adapt to this new playing style easily."
Regarding what has happened with Sporting, he added: "There was a misunderstanding, I never wanted to do something wrong at Sporting as I have always been very thankful to that team that gave me many chances for playing in Europe.
"If I made a mistake, I have already apologised because I didn't want to hurt the feelings of anyone at the club."