United face a battle to land Maguire and will have to shell out in the region of £80m to get him.
This would be more than the world record £75m Liverpool spent on signing Virgil Van Dijk from Southampton last season.
United executive vice chairman Ed Woodward has approached Leicester about signing Maguire.
Boss Jose Mourinho is desperate to make Maguire his fourth summer signing after landing Fred, Diogo Dalot and Lee Grant.
The former Premier League champions have no intention of selling the England ace and still hope he will sign a new deal at the King Power Stadium.
Leicester will only consider selling Maguire, 25, if he makes it clear to them that he wants to go to Old Trafford.
Even then they will demand a fee of £80m for someone who cost them just £17m from Hull 12 months ago.
The Foxes are loathed to lose another star player following Riyad Mahrez’s £60m move to Manchester City earlier this morning.
The Midlands outfit are also under no financial pressure to sell Maguire – and know his value will continue to rocket in coming seasons.
It remains to be seen if United are now willing to spend so much on a centre back when Mourinho already has Eric Bailly, Phil Jones, Chris Smalling, Victor Lindelof and Marcos Rojo at his disposal.
Starsport understands Woodward is becoming concerned by Mourinho’s obsession with stock-piling defenders at Old Trafford – and wants him to sell at least one of them to help fund the arrival of Maguire.
The pressure is also mounting on Woodward as he looks to provide Mourinho with a side capable of challenging for the title again.
He drew a blank when it came to Real Madrid’s Gareth Bale and has also been snubbed by Croatia and Inter Milan ace Ivan Perisic.
Maguire knows his stock has never been higher following his stunning exploits at the World Cup with England.
He is open to a move to United, where he would be guaranteed regular Champions League football and could also treble his wages.
But Maguire is known to be happy in Leicester and will wait to see what terms the club offer him before deciding his next move.