However, Puel has maintained his stance that the playmaker is not for sale in January, and has suggested that a fee of £100m could be required in the summer.
The 56-year-old is quoted by the Leicester Mercury as saying: "It is always the same thing about Riyad. It is just rumours, noise about him and other players.
"We can see Riyad smiling and enjoying his football and enjoying playing with his team-mates and it is the same in training. After the training session, he continues to play head tennis, and I want him to get more rest.
"All the rumours and speculation about Riyad, do the reporters want him to leave the club? It is speculation and we cannot respond to all the speculation with information. Perhaps, in the summer he will cost even more than £100m."
Mahrez has contributed seven goals and seven assists in the Premier League this season.