The Scot was making a name for himself in managerial circles at Championship outfit Preston North End at the time.
He spoke to Old Trafford officials about joining the coaching staff at the Theatre of Dreams, but found himself overlooked.
"I spoke to Sir Alex about the No. 2 job but wasn't offered it and I've gone on to do what I had to do," said Moyes.
"I would have liked the chance to see the man working and be around him.
"Will it be a poisoned chalice at United? I don't know, but that's why you should be talking about the greatness of Fergie. You should be embracing the manager.
"Hopefully, he'll be there for 26 or 27 years. I don't want him to go, I just want him to share the trophies around a bit more!
"I can see myself staying at Everton for 10, 12, 15 years if they want me. Sometimes supporters get fed up with you and want a change, but people realise you're better off with stability.
"They will tell you there was a day when Fergie was nearly gone and they tell you here there was a time when David Moyes was struggling. I bet Fergie didn't feel that way and honestly I never did. If you're doing the job right, you know you'll get there."