The Premier League rivals are set to go head-to-head in the summer transfer window with moves for the defender, according to Adrian Kajumba of the Daily Mirror.
Kajumba noted how Red Devils manager Jose Mourinho has identified Maguire as the player to reinforce his options at the heart of the defence. Meanwhile, City boss Pep Guardiola retains an interest in the 24-year-old, even after spending £57 million to sign Aymeric Laporte from Athletic Bilbao during the January transfer window.
However, Kajumba also pointed out the Foxes would be reluctant to part ways with the defender, who could cost United or City as much as £50 million.
Leicester signed Maguire last summer after the Sheffield native had been relegated with Hull City. He arrived at King Power Stadium to help refresh a central-defensive rotation led by the 33-year-old Robert Huth and the 34-year-old Wes Morgan.
Maguire has endured some shaky moments since joining Leicester, but his performances have improved as the season has progressed.
An aggressive approach to attacking the ball in the air defines Maguire's game, and he is rarely outmuscled in a duel. The England international is also more comfortable in possession than he's often given credit for.
City would welcome the latter quality, with Guardiola insisting every member of his back line is talented on the ball. Laporte and John Stones fit the bill, while Nicolas Otamendi has made strides in this regard since the Catalan's arrival as manager in 2016.
United perhaps have the bigger need for Maguire despite owning a better defensive record than the Citizens. Phil Jones has played well this term but still gets bitten by the injury bug.
Speaking of injuries, an ankle problem has cost Eric Bailly the chance to kick on during his second season at Old Trafford. Mourinho's squad has missed Bailly's pace and power, with Chris Smalling and Marcos Rojo struggling in his absence.
Pairing Maguire with Jones or a fit-again Bailly would give United the kind of defensive bedrock Mourinho's best teams have been built on.
Convincing Leicester to sell won't be easy, although Kajumba named Brighton & Hove Albion centre-back Lewis Dunk as a Foxes target should they choose to cash in on Maguire.