Moyes, who was in charge of Preston North End at the time, held discussions with Ferguson after his then assistant Brian Kidd decided to become manager of Blackburn Rovers in December 1998.
Steve McClaren was eventually handed the job, and Moyes now says that although he would have taken on the role, he is not too disappointed to have missed out.
"I met Fergie in the year they won the Champions League," Moyes told reporters. "He asked me to have a cup of tea with him. He was looking for an assistant. I met him but he gave the job to McClaren.
"I was fine with that because I was enjoying what I was doing at Preston but, if that opportunity had come, I wouldn't have turned it down. Maybe it was a good decision not to do it.
"They went on to win the European Cup and have been very successful since but I'm happy with the way it's worked out for me."
Moyes's Everton travel to Old Trafford to face Ferguson's United this afternoon.