The 25-year-old still has four years remaining on the initial deal he signed when joining the club last summer, but after a solid Premier League campaign he has shot to prominence with his performances at this summer's World Cup.
Maguire has been an integral part of England's run to the semi-finals of the tournament, leading to speculation that the likes of Manchester United, Liverpool and Tottenham Hotspur could look to prise him away from the King Power Stadium.
However, the Leicester Mercury reports that the Foxes are willing to make Maguire one of the highest earners at the club following the departure of Riyad Mahrez, who joined Manchester City on Tuesday.
Jamie Vardy - who could also be in line for a new contract this summer - and Kasper Schmeichel are currently the top earners for Leicester, and Maguire is now expected to be offered a deal which would match the two Premier League title winners.
Maguire played every minute of every Premier League game for Leicester last season.