The Italian guided the Foxes to the top-flight title last season and has apparently pledged his long-term future to the club.
Leicester are yet to confirm the reports Ranieri has agreed to extend his contract beyond the initial three years he signed last summer, when he was a shock appointment.
It is claimed any new contract will not include a release clause.
Ranieri has always stated he was happy at the King Power Stadium and, last season, said he was in no rush to extend his deal despite their improbable success.
He replaced Nigel Pearson last summer and was installed as one of the favourites for the sack, with Leicester 5,000-1 to win the Premier League.
But they lost just three league games all season to claim a shock title by 10 points and will be one of the top seeds in the Champions League draw later this month.
They lost the Community Shield 2-1 to Manchester United at Wembley on Sunday and start the defence of their title at Hull on Saturday.
Jamie Vardy and Kasper Schmeichel have signed new contracts at the Foxes during the summer with Vardy rejecting a move to Arsenal in June after the Gunners triggered his release clause.
Ranieri remains confident Riyad Mahrez will also stay at the champions with last year’s PFA Player of the Year linked with Arsenal.