Ranieri is desperate to avoid uncertainty about Kante dragging on deep into pre-season with Chelsea among the clubs keen to prise the Frenchman away.
The Italian is confident of keeping key playmaker Riyad Mahrez but is less sure about Kante.
Ranieri said: “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.
“I would like now to be sure who stays with me or not, because the friendly matches start now and I have to start to manage and change and try things.”
Ranieri has made regular calls to Kante, 25, who has a release clause of around £20m in the Foxes contract.
And he hinted Chelsea are not the only big club trying to lure the all-action Frenchman.
“Maybe it is not Chelsea, maybe it is another team who made the Champions League,” said Ranieri.
Mahrez – last season’s PFA player of the year – has also been linked with a host of rival clubs but Ranieri said: “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.”
Leicester are in Austria at a pre-season training camp and Ranieri is also in talks about a new deal for himself.
He signed a three-year contract last summer but is likely to be rewarded for last season’s fairytale title success with a four-year, £3m-a-season package.
“I think before we start the season I will sign, but I signed one year ago,” said Ranieri, 64. “I think I will sign but it’s not important for me.”
Star striker Jamie Vardy will link up with the squad in America later this month – they play PSG in Los Angeles on July 30 – after he rejected a move to Arsenal to sign a new four-year deal.
He and Kante have been given extra time off after playing at Euro 2016, but Ranieri says Vardy’s new contract has already boosted the squad.
“It is unbelievable,” said Ranieri. “It was fantastic because Jamie is our point of reference, or one of our points of reference. Of course all his team-mates are happy and gave us a lot of energy to have another good season.”