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."
@solskjaer99, I didn't realise all United fans were this stupid? Why would offering contracts to academy graduates be relevant to 'homegrown' quotas? United DID have a history of developing players. There is also zero evidence that Rojo has anything to do with turtle head. He's a panic buy after your actual targets turned down United.. @abdudelusional.. United have spent the second most net in Europe in the last five windows. That is an official stat. After reading my comment, I tried to amend it but it never came through. I have noticed I put, most, and not second too late. So United have a net spend of nearly £200 million. That dwarfs everyone but PSG. Yet United are still a shambles. Weather I agree with Conn or not, you do, you did. So someone you've referenced several times is highlighting the Glazers. The article mainly relates to how much money they are taking from the club the fans. But you love the Glazers right? David Conn, whom you regularly quote has dismissed everything you say. as I say, most United fans I know, fans who've actually been, actually go are disgusted by the Glazers.. Irelan is on £80k a week at Villa, so he's done ok. Rodwell wasn't fit for City, injured or not, he wasn't reliable. You can't build a team round him. But why do you care? He's not top level. He's not good enough for City. We tried, it didn't work we got our money back.. Tell us all how United wouldn't sack Moyes- charming_man