Mahrez was strongly linked with a move away from the Foxes last summer, but ultimately remained with the former Premier League champions, and has scored seven times and provided eight assists in 22 Premier League fixtures this term.
Chelsea, Arsenal and Liverpool have all been credited with an interest in the Algerian international, but Puel has branded the reports "just speculation".
"I can say always the same thing. Riyad is a valuable player for us and I want to keep him," Puel told reporters. "Of course, no problem with Riyad with his hard work in the training sessions, he is enjoying his football with his teammates and he is playing very well.
"You can see him at the training session this morning, he was smiling. It is amazing to train this player. It is just speculation."
Mahrez is expected to be in the Leicester team that starts against reigning champions Chelsea in the Premier League on Saturday afternoon.