The Foxes reportedly wanted a deal that could have been worth $A170 million for Mahrez, a fee the Premier League leader was unwilling to pay.
Mahrez was consequently resigned to staying at the King Power Stadium and it has been reported that the Algeria winger is yet to return to training since talks collapsed.
Leicester boss Puel confirmed that Mahrez is not in his plans for the weekend, but urged him to return to the fold.
"I think Riyad will be not available for the Saturday game against Manchester City," Puel said.
"I hope he can get his head right and come back with us and work hard. The best way is to come back and enjoy his football.
"Riyad is a magnificent player. He loves football, he loves his relationship with his team-mates, he enjoys his football. I think he needs to come back, to play and touch the ball.
"He loves his football, it is important he comes back."
Despite the distraction and disruption caused by the Mahrez saga, Puel has been impressed with how the rest of his squad has carried on regardless in a professional manner.
"I was impressed in my training session with the quality we can put on the pitch," the Frenchman said. "It is a good feeling; the players have kept their focus about the next games.
"We know it's a difficult situation, but we needed to look forward and to continue this hard work. The squad has good quality, strength and when I saw their attitude in training, they have taken their responsibilities."
Puel has also received the blow of losing Shinji Okazaki to injury.
"[There has been a] little injury with Okazaki, he will not be available," Puel added. "He received a kick on his knee and I think he won't be available for two weeks."