The 25-year-old Professional Football Association (PFA) Player of the Year award scored 17 goals and contributed 11 assists as Leicester won a maiden Premier League title last season, prompting transfer speculation of a move away from the King Power Stadium.
"He has to play better because we are now also in the Champions League and we need something more to play against these big teams," Ranieri told journalists on Thursday. "Now he knows very well what I want and my expectation is higher, not only for Riyad but for all of my players.
"Maybe Riyad could be now a little more free. I saw him during the days, he is a nice guy, always laughing, never was he so anxious or nervous."
Ranieri, whose Leicester side are seeking their first points of the season when they host Arsenal on Saturday, is also confident that midfielder Danny Drinkwater will extend his deal, which currently runs until 2018.
"Danny is very, very close to signing a new contract," he added. "Our owner is very ambitious. He wants to maintain the same spirit and squad."
