According to The Mirror, City boss Pep Guardiola remains interested in signing the £50m-rated defender despite recently acquiring Aymeric Laporte for £57m from Athletic Bilbao.
United manager Jose Mourinho has also ruled out making any more big attacking signings after pipping his city rivals to the signature of Alexis Sanchez in January, with Maguire being the perfect acquisition as he aims to shore up his defense.
The two clubs tussled for months over the signing of Alexis and it looks like the tug-of-war could be reunited this summer as Guardiola will not want to miss out on another player he has been monitoring all season.
Maguire only joined Leicester in the summer for £17m from relegated Hull City and he still has four years to run on his contract so any potential deal will not be cheap.
Leicester fended City off in January with their late approach for Riyad Mahrez and they are expected to stand firm again for another one of their star players.
Since joining the Foxes, Maguire has gone on to win his first England international cap and is expected to be on Gareth Southgate's plane to Russia after asserting himself as one of the Premier League's toughest defenders.
If Leicester do lose their 6'4" central defender, then they will reportedly turn their attention to Brighton's Lewis Dunk.