With Rooney seeking a move away from United this summer following friction between him and Ferguson, exacerbated by the Scot's revelation of the player's determination to leave the club, the former United manager insists that the 27-year-old would now shake his hand, instead blaming the player's advisers for the efforts to force a move to Chelsea.
Asked whether his relationship with Rooney ended badly, Ferguson said: "No, I don't think so. I think if Wayne walked in here today, he would shake my hand."
Asked when they had last shaken hands, Ferguson responded: "The day when we won the league and the winner was presented with the cup. I never fell out with him at any time, you know. Sometimes I would discipline him, but sometimes they all need discipline.
"Wayne is unfortunate in the sense that he is England's big white hope. So therefore, the media is always centred around Wayne. And he has people who advise him. And I think that's where all that's coming from.
"He is back to his form and if in some way I've helped to bring that back, then I've done the right thing - made him aware that he's a great player and we need him. When the club refused to sell him to Chelsea, he realised his only job was Manchester United. And it has brought back his focus. It's brought back his work ethic and his purpose, and, you know, he is playing well again.
"I managed a team and at that particular moment [when his desire to leave was revealed], he wasn't doing particularly well. But now we see him today, he's got his energy back, he's got his purpose back, and he's doing great. So maybe that was a good turning point for the boy, you know?"
While United have been able to keep Rooney at the club, despite the player's issues with the Scot still to be resolved, the rift between Ferguson and Beckham resulted in the midfielder being sold to Real Madrid in 2003.
Before Beckham's departure, the pair had infamously clashed with Ferguson kicking a boot on to Beckham's head after an FA Cup defeat at home against Arsenal, leaving the player with stitches above his eye. Beckham's celebrity lifestyle and marriage to Spice Girl Victoria Adams had left Ferguson exasperated by the player's lack of "focus", but he admits the former England captain became one of the few players to succeed after moving on from United.
"He is an amazing boy," Ferguson said. "I mean how he has created himself. He's an icon for young people. He's fantastic, a wonderful boy. He always had a lovely smile, you know, and he always presents himself well, but as a young kid when I got him at 12 years of age his great desire was to play some of the best football.
"He was a fantastic trainer, practised all the time and at night-time, he would come by with the schoolboys and practise with them. And then of course, his life changed, when he married the girl from the Spice Girls and his focus changed. He got drawn into that celebrity status, you know? And for me, I'm a football man. I'm a football man. He lost the focus, but when we sold him to Real Madrid, he did well."
Ferguson admits he was shocked by Beckham's decision to leave Real for five years in the Major League with LA Galaxy in his early thirties. "I couldn't understand that. I would never do that, you know?
"If I was going to go, I would be making sure he would go to the best, and Real Madrid was the best, I would say, and United. But he reinvented himself.
"He's unbelievable. He really is - and good, well done to him. I mean, he's - you can't argue with the status he has in life. But for me, it would have pleased me more to see him be a great, great player, you know?"
Ferguson confirmed he could have followed Beckham out of Old Trafford in 2003 after being contacted about the manager's job at Chelsea following Abramovich's takeover at Stamford Bridge.
Asked whether Abramovich had ever asked him to manage Chelsea, Ferguson said: "He used an agent when he first came. They approached me and I said, no, no. No chance. I said: 'No chance. Manchester United is my team. My club'."
By that stage of his United career, Ferguson had delivered eight Premier League titles and a European Cup. However, he admits he suffered a crisis of confidence when fans were calling for his head in 1989, before his first trophy - the 1990 FA Cup.
"One or two banners were up saying 'time up' and things like that, but I think it would be true to say that at that period I did lose a little bit of confidence," Ferguson said.
"However, I didn't lose my determination." Ferguson also endured criticism from many United supporters for his public support of the club's owners, the Glazer family.
"Obviously, there's the misconception about the Glazers buying the club and it created sort of ... different factions of Manchester United supporters. They forget that the minute it became a PLC [Public Limited Company], someone was going to buy it.
"The Glazers did that. And then my time with them, they're nothing but supportive. Very strong, single-minded people, but always supportive of the manager and the things that happen in the club.
"They've been very good and I've had absolutely no hesitation supporting the way they're going about the job - very low-key, very seldom, never give me a phone call."
He said that he had no interest in returning to United and that he had full confidence in Moyes. "I'm not interested in managing again or getting myself worked up about Manchester United's results," Ferguson said.
"United are in good hands with David Moyes. He will be fine. He is a good manager."
