Maguire joined Leicester from Hull City last summer, and impressed for the Foxes during the 2017-18 campaign before playing a key role in England's run to the semi-finals of the 2018 World Cup.
The former Sheffield United youngster was believed to be keen on moving to Old Trafford ahead of the new Premier League season, but Leicester managed to keep hold of the 25-year-old.
Maguire has revealed that United were interested in signing him, but the defender "respected" the decision of the Leicester owners to hold firm.
"There was obviously a little bit of interest, you've probably all seen. The owners spoke with me and they reiterated that I wasn't for sale at any price," Maguire told BBC Sport.
"So I respected their decision, they're the ones that gave me the chance to come to Leicester and play for such a great club. So I respect that decision, and I just got my head down and got ready to play the season for Leicester."
Maguire scored a last-minute winner in Leicester's 2-1 victory at Southampton on Saturday afternoon.