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But the Algerian is holding out for a move to Arsenal this month.
Liverpool are ready to splash the cash after selling star man Philippe Coutinho for £142m earlier this week.
Thomas Lemar has been eyed as a potential replacement for the Brazilian.
But reports in France this week suggested a deal for Mahrez was nearing completion.
And according to the Daily Express, Mahrez is in talks with the Reds but would prefer to secure a move to the capital and play under Arsene Wenger instead.
Riyad Mahrez next club: Latest odds
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“Mahrez has long been linked with a move away from Leicester”
The publication reports the player has bought a house in London ahead of a potential deal.
Mahrez has long been linked with a move away from Leicester.
The winger looked destined to leave the King Power Stadium in summer, and was allowed leave from Algeria's national team on deadline day to complete his switch.
And Foxes boss Claude Puel insists Mahrez is not looking to leave the club this month.
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The Frenchman said: "He is a happy player.
"After that it is all speculation.
"There is no problem.
"I want to continue to work with my best players like Riyad."
The Daily Express report no talks have begun between Mahrez and the Gunners.