Sir Alex Ferguson accused Beckham of becoming distracted by his celebrity lifestyle in his recently-released autobiography.
"It's funny, he was one of the first names I was going to call up to be manager. I'm not so sure now," the former England captain said.
Speaking at an exclusive global digital book signing on Facebook today, the 38-year-old insisted he did not want to speak negatively of his former manager:
"All joking aside I wouldn't want to be negative about Sir Alex. He gave me the chance to live my dream."
Beckham also revealed that after leaving Manchester United he could not face watching them play for two years.
Sir Alex Ferguson describes former Manchester United player Roy Keane as having "the most savage tongue you can imagine" in his autobiography.
Addressing the infamous incident when Keane publicly criticised his team-mates on the club's television channel, and him subsequently leaving the club, Sir Alex told ITV News' Mark Austin:
"It was a savage attack on the players. No doubt about that. I was left with having to make the decision about what to do with it.
"I had a great relationship with Roy right up until that summer we went to Portugal....but he overstepped his mark. And what do you do?
"The players would have thought very poorly of me if I hadn't done something that day".
Former Manchester United midfielder Roy Keane has hit back at accusations in Sir Alex Ferguson's new book by suggesting his former manager lacks loyalty.
Speaking on ITV, he said: "He don't think he knows the meaning of the word.
"It doesn't bother me too much what he has to say about me, but to constantly criticise other players at the club who brought him a lot of success, I find very very strange.
"But I certainly won't be losing sleep over it."
He added: "I don't think the manager needs to do it. I'm not sure how many books he's written now, but he has to draw the line eventually. Can you imagine if we never won a trophy what he would have said?"
"It's part of modern life... people like to do books and criticise their ex players", he added.
Former Manchester United manager Sir Alex Ferguson launched his autobiography today, which lifts the lid on his relationship with the club and some of its famous players.
He told ITV News' Mark Austin that the cult of celebrity prevented David Beckham from becoming a footballing legend.
He also spoke about influence of massive player salaries on the game and said "somewhere along the line, the game will get a rude awakening".
On his successor, David Moyes, Sir Alex said that the "hard-working" manager "would be given time" to get things right at United.
Sir Alex Ferguson told ITV News England should be aiming for the quarter-finals in the World Cup and ruled out ever managing the Three Lions.
He told ITV News presenter Mark Austin: "It's not an easy trophy to win. England have won it once on home soil - but usually it's been shared by Italy, Germany and Brazil. Historically it's very difficult.
"But remember, for Scotland to get to the Championship finals is a success. For England, I would think...getting to the quarter-finals would be great...then you want to think about semi-finals etc."
Asked whether he could one day manage the Three Lions, Sir Alex said: "Absolutely no chance of a Scot managing England, trust me - I couldn't go back."
Sir Alex Ferguson told ITV News David Beckham could have been a Manchester United legend but changed after his marriage to Victoria.
He told ITV News presenter Mark Austin: "My take on it is that he could have been in the same position as Giggs and Scholes, twenty years at United, he would have been an absolute legend, in the pantheon of all the great legends we've had."
"Me being a football man, I want to see them totally committed to the team - that waned and went down a bit."
However, the former Manchester United boss did admit that Beckham had become an "icon" and "inspiration for young people" and praised the midfielder for how he "reinvented" himself later in his career.
Sir Alex Ferguson tells Mike Hall that he may not have retired if Manchester United had failed to win the Premier League last season.