Mahrez remains the subject of interest from several clubs, including Spanish champions Barcelona, according to the British media, while Vardy rejected Arsenal and signed a new deal at Leicester last month.
"Only Kante wanted to go -- that's okay. But I understood him, he came from a little team in France and had a fantastic season. I said to him stay with us and have another year with us but he wanted to go," Ranieri told British media.
"Everybody here is happy and, yes, he wants to stay. No other players will go away -- we will stay together. The football continues without Riyad or without Kante but Riyad will stay with us for all of the years.
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"It's important to maintain the group, with the spirit, with the humility -- that's important for me."
Leicester's head of recruitment Steve Walsh, who was instrumental in bringing both Mahrez and Kante to the club, has been heavily linked with the director of football role at Everton.
Ranieri has already lost a major part of his backroom staff when highly-rated scout Ben Wrigglesworth to Arsenal in January and Rob MacKenzie was installed as Tottenham Hotspur's head of talent identification in February.
Leicester will kick off their title defence with a trip to the KC Stadium, where they will face promoted Hull City on Aug. 13.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Amlan Chakraborty)
