The 25 year old defensive midfielder has been heavily tipped to leave the King Power Stadium, with Chelsea reported to have made a £27m bid.
Ranieri said: "We offered Kante a new deal before the Euros. Now I know there are a lot of big teams interested."
Ranieri said that he was "very happy" that Vardy had stayed at the club, and said that Leicester are "ready" to defend their title.
"Doing it again is not possible, but we proved last season that everything is possible," he said.
"There is no pressure on us, we're the champions. The new champions will have to fight against us - not just the new champions but everybody.
"We know it will not be the same but we are ready."