The Daily Star is reporting that the Red Devils will have to eclipse the £75m fee that Liverpool FC spent on Southampton centre-half Virgil van Dijk in the January transfer window.
The same article states that Manchester United executive vice chairman Ed Woodward has been in contact with Leicester over the possibility of signing Maguire this summer.
However, the Foxes do not want to sell Maguire following his excellent performances in the World Cup despite signing the English defender in £17m deal from Hull City last summer.
According to the same story, Leicester will only sell Maguire to Manchester United if the England star makes it clear that he wants to leave the King Power Stadium.
Manchester United finished in second place in the Premier League table last term but the Red Devils ended up 19 point adrift of runaway champions Manchester City.
Mourinho is thought to be keen to improve his defensive options after Sweden international Victor Lindelof struggled during his first Premier League season at Old Trafford.
Ivory Coast international Eric Bailly struggled in his second campaign at the 20-time English champions.
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