Moyes, who was sacked in April 2014 after just 10 months at the United helm, has explained why he decided against pursuing an interest in Maguire, who was playing for boyhood club Sheffield United at the time.
Speaking to TalkSport, Moyes said: "We didn't try to sign him [when at Man United] but we flagged him up at that time.
"I was very aware of the players in the lower leagues and had a made good career out of bringing them to Everton - whether that be Tim Cahill or all the ones we did through the years.
"Harry Maguire was another one I recognised. He played against Preston North End at home in a league game and I watched him and thought he played really well but at that time he was really big – he had a big a***.
"You thought 'my goodness, how big is Harry going to be' because he was a relatively young boy at that time.
"So for us to go and buy another young centre-half wasn't the biggest thing we needed at the time.
"And Harry Maguire has had to go on his journey. Sometimes the players need the journey to get to where they have to go. He might have struggled then."