The England international has been identified as a key target for Ole Gunnar Solskjaer’s squad revamp.
However, the Foxes are under no pressure to sell the centre-back, who penned a new contract until 2023 last summer after an impressive World Cup campaign in Russia.
ESPN FCsources have said that United will continue to push for the signature of the centre-back despite not wanting to meet Leicester’s demands.
The outlet also reports that the 26-year-old would be open to a move to a top-six Premier League club if a fee is agreed with his current employers.
Maguire was on the Old Trafford club’s radar last summer too and they have continued to keep tabs on his situation, with rivals Manchester City also showing interest.
United hope to reach a compromise with the King Power outfit at a lower price as they refuse to drop their interest altogether.
Napoli’s Kalidou Koulibaly is an alternative being considered if Leicester refuse to lower their demands, while United are also chasing Crystal Palace right-back Aaron Wan-Bissaka.