The Foxes want more than the £75m Liverpool paid Southampton for Virgil van Dijk earlier this year to part with Maguire, who has four years left on his contract.
United boss Mourinho is ready to sell Marcos Rojo to Everton for £20m to help finance the move for the Sheffield United academy graduate.
Tottenham defender Toby Alderweireld and Barcelona’s Colombian World Cup star Yerry Mina are also targets ahead of Thursday’s transfer deadline, just 24 hours before United’s Premier League season begins against Leicester at Old Trafford.
According to EXPRESS SPORTS Maguire has emerged as United’s prime target to bolster their backline having starred in England’s run to the World Cup semi-finals.
The 25-year-old played on the left side of the Three Lions defence as Gareth Southgate guided his team to the last four in Russia.
And a move to United would represent the next step in a remarkable rise for Maguire, who was playing Championship football as recently in 2016.
Former England boss Sam Allardyce recently discussed the prospect of Maguire heading to United to play under Mourinho.
“It depends what coach he gets next,” said Allardyce, when asked about the prospective switch.
“If you get a good coach, they both take into consideration and stop this palaver about centre halves being good on the ball.
“You’ve got to be a very good defender if you’re going to play for Manchester United.
“I remember speaking to Sir Alex Ferguson and Brian Kidd about this. If you’re going to play for Manchester United you’ve got to be able to handle one-on-one.
“Manchester United need to go and break teams down and to commit, so if you’re a central defender you have to sit there one-on-one and be able to cope with it.
“This means you have to be one of the best defenders in the league.
“You can still teach Harry that defensive side of the game. Everybody needs to keep being reminded about what their responsibilities are.
“He’s certainly got the potential to get even better.”
Maguire would join fellow defenders Chris Smalling, Phil Jones, Eric Bailly and Victor Lindelof at United.
United hero Dimitar Berbatov has offered his backing to a raid on Leicester for the former Wigan loanee.
“Manchester United need to sign a defender – probably Maguire from Leicester – he had a great World Cup, simply because of the way he controlled the ball and the vision he has on the pitch,” said Berbatov.
“He has the ability of passing like a midfielder and stays calm under pressure. He would be a great addition to the squad.”
Maguire and his representatives have made no comment so far on wanting to join Manchester United.