The three-cap England international has been at the King Power Stadium for less than a season, having joined from Hull City last June in a £12m deal up front.
Maguire has impressed in the heart of defence for the Foxes this term, though, and The Mirror suggests that United and City are now about to battle it out for his signature.
City moved to bring in a new centre-back during the January window, signing Aymeric Laporte from Athletic Bilbao for a club-record fee, but the report claims that Pep Guardiola still retains an interest.
Arch-rivals United are known to be on the lookout for defensive options, meanwhile, and £50m-rated Maguire - under contract in the East Midlands until 2022 - is seen as a viable choice.
Leicester are reportedly reluctant to sell and will do their best to fend off any interest, however, having done likewise when the Citizens made their move for Riyad Mahrez last month.