The 26-year-old has enjoyed another fine season with the Foxes, but is expected to leave the club this summer.
The Sun claim it will take a record fee for a defender to tempt Brendan Rodgers into selling Maguire, who is rated at £60million.
Chelsea are believed to be in the market for a leader in defence, while Manchester United and Arsenal are set to address their leaky backline, which has conceded 52 and 50 Premier League goals, respectively, this season.
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Spurs, who could lose Toby Alderweireld for just £25million, are also reportedly keen on a deal for the England star.
It is understood Leicester will demand a huge fee after Manchester City paid £50million-plus for defenders Kyle Walker and John Stones.
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