The Red Devils are the clear favourites to land Maguire this summer.
But Manchester City remain in the hunt for the 26-year-old at present as they look to strengthen their title-winning side further.
Starsport understands Pep Guardiola’s men would need to offload two players if they were to part ways with £80m for the defender.
And Sky Sports man Dharmesh Sheth reports that should Nicolas Otamendi leave, City will look to swoop for Maguire.
“Maybe City are not willing to get into a bidding war with United,” Sheth said on the Transfer Talk podcast.
“They’ve done it before, they know what a player’s worth.
“Have they pulled out of the Maguire deal? We don’t know yet.
“But if you look at what Pep Guardiola’s been saying, he was kind of noncommittal about the central defensive situation.
“He doesn’t know if the players who are there are going to stay or if they’re going to bring anyone else in.
“The noises we’re getting from City is that Otamendi is the key here.
“If he was to go, then perhaps they would go all out for a central defender, perhaps Harry Maguire.
“But Otamendi’s given no indication that he wants to leave City.
“I think he now thinks with Kompany having left the club, he will get more opportunities to play.”
Maguire featured against Scunthorpe earlier this week and has been praised for his professionalism.
But the Foxes star is said to disagree with Leicester chiefs behind the scenes.
According to Sky Sports reporter Kaveh Solhekol, the England international is not convinced he is worth as much as Leicester are demanding this summer.
“I don’t think United want to make him the most expensive defender in the world,” he told the Transfer Talk podcast.
“We’re also being told that Maguire himself is, I have to choose my words carefully, I don’t think when he looks in the mirror he sees a £70m player.
“I’m sure he thinks he’s a very, very good player but I don’t think he thinks he’s worth what Leicester are asking for him at £80m.
“So that’s the situation we are at at the moment.”