According to Leicester Mercury, the contract would make Maguire one of the highest paid players at the club, with manager Claude Puel wanting to build his Leicester side around the 25-year-old.
Maguire signed a five-year contract after joining from Hull City last summer in a deal worth up to £17m, and played every minute of Leicester's Premier League season. However, his impressive form for both club and country seem to have earned Maguire a big pay rise.
Following winger Riyad Mahrez's £60m move to Manchester City, Puel is keen to ensure that the rest of his key players are not targeted this summer, and will also be opening talks with Jamie Vardy over a new deal.
Vardy and goalkeeper Kasper Schmeichel are currently Leicester's two highest earners following Mahrez's departure, and Maguire is expected to be offered a similar deal to reflect his importance to the side.
Maguire has been a hugely important player for England during their impressive World Cup campaign. He managed to get on the score sheet in England's fantastic 2-0 victory over Sweden in the quarter-final and has consistently looked strong defensively, despite England only managing to keep one clean sheet in their five games so far.
His move from Hull City to Leicester City was fuelled by his desire to make an impact for the England national team, and it appears as though Maguire's determination has been rewarded.
He has featured in every game for his country at the World Cup so far and has only missed 45 minutes of the tournament, during England's clash with Belgium, which saw several key players rested.