According to British media reports, Kante, who joined Leicester from French Ligue 1 side Caen last August, could be lured away by top clubs like Chelsea, Real Madrid and Paris St Germain.
The 25-year-old Frenchman played a pivotal role in Leicester's title-winning season and was rewarded with a call-up to his country's squad at the European Championship, where the hosts lost the final to Portugal.
Vardy signs new contract with Leicester
"I would like to understand if he stays with me or not. I speak often with him. If one is not happy with me I prefer that he goes," Ranieri told British media.
"We offered a new contract to him, he went away because he wanted to finish Euro 2016, and now there is so much speculation around him.
"I don't want to lose him but I can understand if he wants to go."
Ranieri named England's Manager of the Year
Ranieri said he is optimistic of hanging on to Algeria international winger Riyad Mahrez, who won the PFA Player of the Year award last campaign.
"I am very confident with him. He stays here with us. He enjoys it and is not a man saying 'coach I want to go'. He is happy," Ranieri added.
Leicester, who will make their first Champions League appearance in the upcoming season, begin their Premier League title defence with a trip to promoted Hull City on August 13.
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