With Vardy and winger Riyad Mahrez firing on all cylinders in the early part of the new season, Leicester are fifth after nine games, three points behind Arsenal in second.
Top scorer Vardy has three more goals than his closest competitors Alexis Sanchez, Sergio Aguero and Georginio Wijnaldum, while team mate Mahrez has netted five times.
"Nobody goes in January -- not Riyad (Mahrez), not Jamie, not (Jeffrey) Schlupp, nobody," Ranieri said.
"We want to improve and to achieve our goal as soon as possible. I need, the club needs and the fans need all our best players.
"We are waiting for the bigger clubs but this is only speculation and we won't sell him," he added.
A goal against Crystal Palace on Saturday would see Vardy become the eighth player to score in seven successive Premier League matches.
Ranieri said Vardy had to keep delivering the performances, even when the goals dry up.
"He is playing really well and I hope he can continue but football is strange," said Ranieri.
"It's not important to think about goals or no goals. It's important to think about how he plays for the team. If he can continue in this way it would be fantastic."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Peter Rutherford)
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