Algeria international Mahrez was hoping for a move away from the King Power Stadium last summer but, despite interest from Roma and Arsenal, he remained with the former Premier League champions.
The 26-year-old has been in decent form this season, scoring seven times and providing eight assists from 22 league matches, and the likes of Chelsea, Liverpool and the Gunners have all been credited with an interest.
However, Puel, who has hinted other players could leave, insists he has no intention to sell the winger this month and is keeping his fingers crossed the club can hold onto their prized asset.
"I can say always the same thing. Riyad is a valuable player for us and I want to keep him," he said. "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."