Maddison has played a crucial role in Leicester City's emergence as Premier League title contenders this season.
The Foxes find themselves second, six points clear of Manchester City in third place.
Their run of form is superior even to that of their famous title-winning season in 2015/16.
Brendan Rodgers has been praised for his management and was rewarded last week with a new five and half year deal.
This was reportedly frustrating for Arsenal, who were eyeing up the Northern Irishman to replace the sacked Unai Emery.
Leicester are now hoping to do the same with Maddison, who is close to signing a bumper contract extension, according to The Athletic.
Since moving to the King Power Stadium from Norwich in 2018, Maddison's reputation has grown such that he earned his first England call-up.
The 23-year-old has also attracted interest from other Premier League clubs and is most heavily linked to Manchester United.
United are understood to be keen to add more creativity to their ranks and see Maddison as the ideal signing.
Having joined Leicester for £20m, it's believed Maddison could now cost at least three times that amount.
The Coventry-born midfielder now has five goals and three assists in the league this season.
Leicester are also reportedly trying to tie-down Maddison's teammate Caglar Soyuncu.
The Turkish defender has been impressive in replacing the departed Harry Maguire this season and it's believed he's being tracked by Manchester City.
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