"The transfer market is finished for us. I am only interested in my players and no-one goes away. Business is finished," Ranieri told reporters.
Vardy and Mahrez have scored 28 of Leicester's 37 Premier League goals this season, lifting them to second in the table, two points behind leaders Arsenal.
"You think with one big player we'll arrive in the Champions League? Possibly, but you can't be sure," Ranieri said.
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"Step by step we are building to try in the future to fight for the Champions League. Now this is a crazy league and we fight to achieve the maximum."
Leicester travel to play fourth-placed Tottenham Hotspur on Wednesday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
