Maguire, 25, has been subject to interest from United manager Jose Mourinho since impressing in his debut campaign at the King Power Stadium.
As a rare breed of ball-playing English central defenders, the robust Foxes star impressed with England during their run to the semi-final of 2018.
However, with manager Claude Puel's already losing 2015/16 PFA Player of the Year Riyad Mahrez, the club have reportedly set a £80m (R1.37b) price-tag on the former Sheffield United defender - according to Starsport.
This would eclipse the deal that saw Virgil van Dijk joining Liverpool from Southampton in January.
When pressed for an answer to the recent reports in English media linking the Three Lions defender to Old Trafford, the Frenchmen claimed the player in question, alongside Jamie Vardy, 'is Leicester'.
"I am confident about the presence of Harry for this season. He is a very good player for us," Puel told Sky Sports News.
"I was not surprised about his performance during this World Cup. We saw his progress during the second half of the season.
"Of course for us he is a very good player -- I wait for him with impatience because we need Harry and we need also Jamie [Vardy] because they are Leicester."
"If we lose a player just a few days before the beginning of the season without the ability to replace him... To change the scene before the start of the season is not possible."