United moved ahead rivals Manchester City in the chase for the England defender by increasing their offer to £70m, following the initial £65m that both clubs had indicated they would be happy to pay last month.
But Leicester have made it clear they are not interested in selling at that price, especially after seeing United pay £50m for Aaron Wan-Bissaka, who they feel cannot compare to Maguire in proven international quality and experience.
Aiyawatt Srivaddhanaprabha, Leicester's owner, would need to personally sign off any deal for Maguire, who still has four years left on his contract and is seen as a key asset in their squad.
United have already signed two home-grown youngsters in Daniel James and Aaron Wan-Bisaaka.
They have also made an enquiry into signing Southampton midfielder Mario Lemina, Sky Sports News understands.
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