According to The Independent, United have moved into pole position in the race to sign Maddison.
It's thought that Liverpool, Manchester City and Tottenham are all keen.
But Ole Gunnar Solskjaer has reportedly made his their mission to snap up the highly-rated 22-year-old.
Maddison scored seven goals and assisted seven more in a hugely impressive debut season at Leicester.
Leicester bought Maddison for £20 million from Norwich City last summer.
The attacking midfielder fits the mould of United's youth-orientated transfer policy set out by Solskjaer and Ed Woodward.
Maddison wouldn't come cheap, however, with the Englishman believed to be valued around the £60 million mark.
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