Real Madrid have contacted Mahrez’s representatives in a bid to sign the Algerian international before the transfer window closes next month.
Bale’s future at Real Madrid is unclear, having fallen out of favour under the Los Blancos manager, Zinedine Zidane.
He has two years left on his current contract with Real.
His time in Real Madrid has not gone as planned, as he has been frozen out by Zidane.
The 31-year-old made just 20 appearances for Real Madrid last season and only two of those came after football’s restart following COVID-19 lockdown.