United were keen to sign him last summer when Jose Mourinho was manager but club chiefs were put off by Leicester’s reported £65million valuation.
They are desperate for a new centre-back as current boss Ole Gunnar Solskjaer looks to overhaul his struggling squad at the end of a disappointing season.
Leicester face Chelsea in their final game of the season tomorrow and the report claims it will also be the defender’s final game in a Leicester shirt.
Chelsea will only be able to sign him if they can get their two-window transfer ban overturned.
But If they can, the Blues and Spurs will be able to offer the England international Champions League football next season, while Arsenal will be able to do the same if they win the Europa League.
United, meanwhile, failed to qualify for Europe’s top competition after a lacklustre 1-1 draw at Huddersfield in their last Premier League outing.
And that might tip the odds in favour of the other three as Maguire has previously admitted it is his dream to play in the Champions League.
Speaking in October last year, Maguire said: ”Everyone wants to play at the top level, everyone wants to play in the biggest tournaments in the world, so obviously the Champions League is one.”
Leicester boss Brendan Rodgers admits it might be difficult to keep him at the King Power Stadium if the division’s biggest clubs do come calling.
However, he insists he will do everything he can to convince him to stay.
“There have been discussions,” he said. “We just have to wait and see. I’d love him to stay. It depends on the player.”
If Leicester are forced to sell, the report from The Sun claims it will take a British record fee to get him.
The current record stands at the £50m Manchester City paid for Kyle Walker and John Stones.
Leicester could also lose midfielder Youri Tielemans in the summer.
The 22-year-old has impressed since joining on loan from Monaco in January.
Like Maguire, his performances have altered most of the Premier League’s top six.