The 34-year-old is weighing up whether to play on beyond the end of his contract in the summer but recounts how the Red Devils had been interested in him while he was still at rivals Manchester City.
"It's true – my adviser had a conversation with United in 2010, shortly before I came to Cardiff on loan," he told the Daily Mirror. "It was great to feel wanted and I would have loved to do it but it was never going to be allowed to happen.
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"After Carlos Tevez had moved in the opposite direction the year before, I didn't expect anything to come of it.
"Actually, there was a link with Sir Alex as far back as 2002, when my representatives went to see him at United’s training ground, with a view to a move going ahead but Newcastle had just qualified for the Champions League, I loved playing for Sir Bobby Robson and had just been offered a new contract there. To be honest, I used an enquiry from United to hold out for a better deal."
Bellamy also explained how Moyes, then at Everton, made more than one attempt to bring him in but had failed to convince him.
"When I was leaving Newcastle, Moyes came to see me and tried to sign me for Everton," he recalled. "He made me feel the most wanted man on earth.
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"He had this list of rules, saying I was to do this and I had to do that. He was saying: 'If I do sign you, this is what I expect.' It was different to the first meeting and made me wonder if he was totally convinced about signing me at all.
"It wasn't anything to do with lifestyle. It was more like: 'If I switch you to right wing after 60 minutes, I don't want you shaking your head.'
"Then Bill Kenwright, the Everton chairman, was on the phone, saying the medical had been arranged, but I said to my adviser: 'This doesn't feel right' and we called it off.
"A few months later, David rang up and apologised, saying he should have got the deal done, which was very big of him. He tried to sign me again when I was at West Ham and again when I was at Manchester City."