Moyes joined Cambridge from Celtic as a 20-year-old after making 24 appearances for his boyhood club.
Having taken his coaching badges at the age of 22, Moyes was ready for his first managerial spell which came with Preston in 1998.
And Fallon has revealed how Moyes displayed his potential for coaching even in his young days at Abbey Stadium.
Asked if he was a coach in the making as a young player, Fallon told TribalFootball.com: "Definitely, he was very mature for his age with the attitude and behaviour of a much more experienced professional.
"He would analyse things to a great depth but was a popular member of the squad, well-liked by all.
"No surprise that he went into the coaching/management side at a relatively young age."
Unfortunately for the Scotsman, his dream job at Old Trafford lasted just eight months.
He has since taken West Ham to a sixth-placed finish in the Premier League, securing Europa League football for next season.
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