“It is one thing to play for Leicester and another to play at the highest level,” Ranieri told The Sun. “When you arrive at the top, when you play well it is normal, so you must do something more.
“It is another very important step so it is important he [Mahrez] grows up with me. It is a normal thing for players who want to grow up that big clubs are asking about you.
“But if it makes you ‘strange’ then you aren’t a big talent. And I believe Riyad and Vardy are very big talents.”
Mahrez joined Leicester from French club Le Havre in January 2014 and has been one of the best players for them.
The 24-year-old has been playing brilliantly this campaign and has been one of the best players in the Premier League.
The former Quimper man has scored seven goals and created 23 chances in 10 league appearances so far this season.
Mahrez has a pass accuracy of 74% and a shot accuracy of 61%, and has won 11 headers, 36 dribbles and nine tackles.
Leicester are third in the Premier League table at the moment with 22 points from 11 matches, just three points behind leaders Manchester City.