The 14-goal winger is likely to stay at the King Power Stadium in January despite being linked with a move away.
Premier League leaders Leicester are not interested in selling Mahrez, who signed a new four-year deal in August, and Ranieri knows the Algeria international needs to handle the extra pressure ahead of the January transfer window.
He said: "He wants to stay with us, we want to keep him and that's it. He has to improve and when he improves, the team improves and when that happens why would he want to go away? He's a king here.
"He can grow with the team because if you stay at the bottom and fight no-one knows you but now everybody is talking about you and that is maybe a bit of pressure.
"You have to manage this kind of pressure. It's important for him to manage this stress. It's important he understands on the pitch is one thing and the TVs and newspapers are another thing."