Rodgers did not mention United by name but said a “huge club” were interested in the 26-year-old England centre-back.
He said: “Harry’s a top quality player and no-one has come near the valuation to tempt the club to sell.”
Maguire featured in Leicester’s 1-0 friendly win at Scunthorpe on Tuesday.
Striker Ayoze Perez, who signed for £30m from Newcastle this month, scored the only goal.
Rodgers added: “The other club interested is a huge club, but he’s a really good guy. I’ve been in this position a number of times and it’s never easy but he’s taken part in everything and hasn’t showed anything other than sheer professionalism.
“You’ve seen that tonight with the 45 minutes he played.”
Asked by Sky Sports News about potential replacements should Maguire leave, Rodgers added: “The club have been very good. If we lose him, we’d have a number of targets we’d look at.”
The defender, who helped England reach the World Cup semi-finals in 2018, signed a five-year contract with the Foxes last September.