Both Liverpool and Arsenal have been regularly linked with a move for the Algerian international, who submitted a transfer request in the summer without a move ever materialising.
There have been numerous reports over the last few weeks that linked the Reds with a move for an attacking midfielder after the big-money departure of Philippe Coutinho to Barcelona.
However, Puel has made clear that the Brazilian's replacement won't be Mahrez - and he believes that the 26-year-old now wants to stay at Leicester.
“He's enjoying playing for Leicester with his team-mates,” Puel said.
“This is the most important thing - we have this good feeling that the player wants to stay with us.