The England international has seen his stock rise over the past 12 months since his move to Leicester from Hull City in a £12m deal, with the fee set to rise to £17m in add ons.
Former Sheffield United defender Maguire netted two goals in 38 games in the Premier League last season to establish himself as a key member of the Leicester team.
Maguire was one of England’s top performers at the World Cup as Gareth Southgate’s side reached the semi-finals before a 2-1 extra-time loss to Croatia.
The 25-year-old scored in England’s 2-0 victory over Sweden before their disappointing exit in the last four.
Sky Sports News reporter Sheth played down Manchester United’s chances of signing Maguire in the current transfer window.
“I wonder how much he will cost after the World Cup,” Sheth told the Transfer Talk podcast.
“He will cost a lot of money. Man United are in the market to sign a centre-half.”
Manchester United finished in second place in the Premier League table last season after the Red Devils ended up 19 points adrift of champions Manchester City.
The 20-time English champions haven’t won the Premier League title since 2013 in Sir Alex Ferguson’s final season in charge.
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