Their elevated profile has already led to speculation that they could be snapped up by soccer's more traditional powers over the close season but Ranieri urged them to stay on for Leicester's maiden Champions League campaign.
"If they are intelligent, they stay with us another year," Ranieri told the BBC after Leicester celebrated their triumph with a 3-1 victory over Everton on Saturday.
"They know the Champions League is very difficult. Then after this next experience they can go.
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"If they ask me something, I say 'stay with me'. But if somebody comes to me and says 'I'd like to go' then go because I want only happy players with me."
Captain Wes Morgan said it had been "unbelievable" to raise the Premier League trophy in front of the ecstatic Leicester fans at King Power Stadium.
"I had to hold back the tears, I held them back and lifted it up - it was the best feeling in the world," he said.
"Hopefully, we can crack on from here. It is a big, big season next season but I want to enjoy the moment.
"It's like a dream but now it's a reality and you just want to enjoy it."
Ranieri accepted that next season would be a challenge for a club that were involved in a battle against relegation 12 months ago but urged the fans to continue to believe in him and his players.
"We know very well next season everything will be different," the Italian said. "But the fans are dreaming - keep dreaming. Why wake up?"
(Writing by Nick Mulvenney, editing by Greg Stutchbury)
