In the summer of 2015, the Foxes were attempting to replace Argentine veteran Esteban Cambiasso who was leaving the King Power Stadium for Olympiakos.
It proved a masterstroke as Frenchman Kante was one of the stars of last season as Leicester remarkably won the title before he was sold to Chelsea last summer.
Ranieri said as a guest on Sky Sports' Monday Night Football: "We were looking at another international player to put there. We lost Cambiasso, who was the main man in the middle.
"He arranged everything and was an experienced player, who calmed the dressing room.
"I tried to keep Esteban Cambiasso here, but he said no, he wanted to go away.
"We wanted an international player, but this player didn't choose Leicester, he chose another country and another club, a big club.
"So in the end we had Kante and Clasie. Steve Walsh told me these two names.
"I watched Kante two or three times, and said Kante. At the start I put him on the left wing! Slowly I started with him there, but after I put him the middle. How can I not put him in the team?"