It was noted by Sky Sports on Thursday that the Red Devils had made their move for the England international defender and valued the 25-year-old in the region of £65 million.
However, it was added that Leicester have no appetite to sell the player, and according to Jeremy Cross of the Daily Star, United would have to part with a staggering £80 million if they want to get the move secured before the end of the transfer window.
"[Manager Jose Mourinho] has told United chiefs to complete a deal before the transfer window closes on August 9—but Woodward’s approach has been greeted with a lukewarm response from the Foxes," added Cross. "...The Midlands outfit are also under no financial pressure to sell Maguire—and know his value will continue to rocket in coming seasons."
Still, Daniel Storey of Football365 doesn't think the Red Devils should be putting forward a massive outlay for the defender:
Maguire has only been a Leicester player for a year, having signed from Hull City last summer for a £17 million fee. His reported current value is indicative of a footballer who has made massive strides in the past 12 months.
The centre-back was named as the Foxes' Player of the Year after a string of commanding displays in defence. Maguire tends to get his head to so many balls, can shift across the ground and gets supporters out of their seats with his forays forward from the back.
His showings for Leicester lead to a place in the England team at the FIFA World Cup, and Maguire was vital in the Three Lions making it into the semi-finals of the competition for the first time since 1990.
Journalist Liam Canning wondered whether United's pursuit of the player is in reaction to his displays in Russia:
There's no doubt United need reinforcements in defence, with Eric Bailly and Victor Lindelof being hit-and-miss since their big-money arrivals. Phil Jones, Chris Smalling and Marcos Rojo have also failed to convince fully under Mourinho.
Still, Samuel Luckhurst of the Manchester Evening News thinks United could do better business than Maguire:
The Leicester man would improve United's defence and potentially be a pillar at the back for years to come. Still, there are some weaknesses in his game, and as such a world-record fee would represent a massive gamble by the Red Devils.
With the window set to shut in less than two weeks, the pressure is on United to get reinforcements to facilitate a title challenge. But being so close to the start of the 2018-19 season, they will no doubt be faced with paying a premium for any key targets.