The Algeria international has enjoyed a fine return to form this season, contributing to 14 goals in his last 18 appearances in all competitions.
Mahrez has since been linked with moves to the likes of Arsenal and Liverpool as both clubs seek replacements for Alexis Sanchez and Philippe Coutinho, respectively.
The Express have claimed that Mahrez has in fact had talks with Liverpool over a move to Anfield, but that he would prefer to join Arsenal, having seen a move to north London previously collapse.
However, both clubs must first convince Leicester to part ways with a player they value at £50m [The Mirror], and manager Claude Puel is refusing to contemplate Mahrez's departure.
"It's not a question in our mind," he said, according to Sky Sports. "All the noise is just speculation.
"Of course we are in the transfer window and it's normal for all the best players [to be linked with transfers], but I'm not afraid about this because there's a fantastic spirit and good attitude in this squad.
"I have confidence in Riyad. We spoke a lot with him, [about] different things, and often about football, because he likes football a lot. He is now with good maturity, good experience of life, and we can see this in this game.
"He has a fantastic influence on the team, a valuable player for the team. We can see he is enjoying his football and is happy with his teammates and with us. It's important for us to keep our best players.
"The good ambition for him is to continue this hard work, to show his consistency game after game, until the end of the season.
"He has come back at a good level: he is clinical, with assists, with goals, and it's important he continues this work and shows people the player he is, without the ball [and] with it. He is making progress. It's a good thing of course [that] he continues all season with us."
After playing a central role in Leicester winning the Premier League title in 2015-16, Mahrez endured a poor campaign last term and in the summer submitted a transfer request in an effort to engineer a move away from the King Power Stadium.
The Foxes' valuation of the schemer ensured that he remained in the East Midlands, where he has played a central role during Puel's opening months in charge.
Whether Leicester will be able to hold off the mounting interest in Mahrez during the second half of the January window remains to be seen, with both Arsenal and Liverpool desperate for fresh attacking resources.
Arsenal are destined to lose Sanchez to Manchester United this week, while Liverpool have £142m to spend from the sale of Coutinho to Barcelona. Champions League qualification potentially hinges on both sides' ability to bring in new faces.