Leicester are demanding a world-record £85million for their star player and The Sun say he vented his anger to the rest of the Foxes squad while away on France for pre-season training.
Both United and City have bid £70m for the 26-year-old but Leicester want a fee that would make him the world’s most expensive defender – surpassing the £75m Liverpool paid Southampton for Virgil van Dijk.
Maguire is reported to think their valuation is unrealistic and pointed to the impending move of Matthijs de Ligt to Juventus as proof.
Ajax are happy to sell 19-year-old De Ligt – the most sought-after defender in world football – to the Italian giants for around £58m.
And Maguire feels the current offers that are currently on the table for him are fair.
City are unwilling to increase their bid but United would be happy to pay £75m.
While Maguire signed a five-year contract last year, the reports from The Sun says they came to a gentlemen’s agreement that Leicester would sell if a top club came in for him.
Maguire has made no secret of his desire to play at the highest level and his stock has never been higher after two stunning seasons at the King Power.
He has also become an England regular and was a star for Gareth Southgate’s England side as they reached the World Cup semi-finals last summer.
Reports that emerged on Saturday night suggest he has also told manager Brendan Rodgers of his intention to leave.
As it stands, Maguire is set to play in Leicester’s pre-season friendly with Scunthorpe on Tuesday night.
Meanwhile, United are currently in Australia on their pre-season tour and he could yet join them out there if an agreement can be made.
Signing a new centre-back remains a top priority for manager Ole Gunnar Solskjaer.
Former boss Jose Mourinho was keen to take Maguire last summer but club chiefs baulked at the asking price which was £60m at the time.
However, they are said to be determined not to miss out on his signature at the second time of asking.