Moyes lasted just nine months in the job after being appointed.
He told The Coaches' Voice: "In my last year or two at Everton, I had been getting approached by many big clubs. The majority of the big clubs in England had all at some time made contact with me.
"It wasn't anything that I was really that interested in. A big Spanish team as well had contacted me but I had always said I would see out my contract at Everton. But out of the blue, Manchester United came for me.
"If you look at Manchester United's history and Manchester United's history of selecting managers, it tended to be... well, really in my time it had only been Sir Alex, but Sir Alex had been really successful at Aberdeen. But you wouldn't have said Sir Alex was the biggest name out there. I think United followed a pattern of picking what they thought was the right fit for their club, a person who they saw as the right way to go.
"They had real good values at Manchester United. I think when I was chosen that I fitted the values that Manchester United had. Young players, hard-working, determination, but also being able to coach and work with players and I believe that was the reason that Manchester United chose me."