The Red Devils have submitted a £70-million offer for the Leicester City center-back, sources told Rob Dawson of ESPN. The bid is likely to be rejected, though, with Dawson noting the Foxes value the England international at £80 million.
United's pursuit of the 2018 World Cup star is also complicated by their city rivals. Manchester City have been linked with a move for the 26-year-old, who reportedly prefers a switch to the Etihad because of the club's ability to offer him Champions League football this season.
United could propose a cash-plus-player transaction in order to sweeten the deal and convince Leicester to part with their big-ticket defender, though such an offer hasn't been presented as of yet.
The Red Devils have long been linked with Maguire dating back to Jose Mourinho's tenure; despite the Portuguese manager's best efforts to sign him last summer, the club's brass was unwilling to meet Leicester's valuation.
Current bench boss Ole Gunnar Solskjaer is still in need of the defensive reinforcements his predecessor craved.
Victor Lindelof eventually settled in as United's most reliable defender last season, but there are questions surrounding both the future and overall ability of the club's remaining options in the heart of the defense; Eric Bailly, Chris Smalling, Phil Jones, and Marcos Rojo have all struggled to varying degrees, while Axel Tuanzebe is only 21 years old.