Kante, signed last summer from Caen for £5.6million, was a revelation during his maiden season in the Barclays Premier League as his energetic, combative performances in the middle of the park were key to Leicester's surprise title success.
Such displays saw the 25-year-old named on the six-man shortlist for the PFA Players' Player of the Year award - won by Foxes team-mate Riyad Mahrez - and brought him to the attention of Europe's biggest clubs, with Real Madrid coach Zinedine Zidane speaking of his admiration for the player while Chelsea are reportedly readying an offer in the region of £29million
Anticipating such interest, Leicester offered Kante an improved deal before he went off to represent host nation France at the European Championship.
Speaking to BBC Radio Leicester on the club's pre-season trip to Austria, Ranieri said: "We offered Kante a new deal before he went to the Euros. Now I know there are a lot of big teams interested. It's in his hands."
Leicester will hope Kante follows the lead of team-mate Jamie Vardy who prior to Euro 2016 turned down the chance to join Arsenal in favour of signing a contract extension with Ranieri's side.
Meanwhile, Vardy has undergone a successful operation on the wrist injury he played through for much of last season.
The 29-year-old striker, who scored 24 Premier League goals during the 2015-16 campaign, suffered t wo broken bones and had to wear a protective cast during games
He delayed going under the knife to help Leicester in their title run-in and then postponed surgery again after being named in the England squad
Vardy has now had the procedure and is expected to link up with his team-mates when they fly to America later this month for the International Champions Cup, where they face Paris St Germain in Los Angeles
Source: PA