The Manchester Evening News says City have made Maguire their top target to replace Vincent Kompany this summer.
The Blues are in the market for a central defender following Kompany's decision to walk away from the Etihad after 11 years at the club, with Nicolas Otamendi's future also uncertain as he seeks more regular first-team football.
City have identified Maguire as the ideal candidate to fill the void, but the Foxes won't let him go cheaply. The 26-year-old signed a new five-year contract at the King Power Stadium back in September 2018 and Leicester's hand is strong when it comes to doing a deal.
Leicester are likely to demand a world-record fee for a central defender, eclipsing the £75million fee that Liverpool paid for Virgil van Dijk 18 months ago, and City may be reluctant to pay such a large figure, which would shatter their own transfer record of £60million for Riyad Mahrez a year ago.