The Algerian, however, described assumptions about his absence from the club as "completely untrue".
He appeared as a second-half substitute in Leicester's 5-1 Premier League defeat at Manchester City last weekend and is expected to start their FA Cup tie against Sheffield United on Friday after showing improvement in training.
When Puel was asked if he thought Mahrez was back to his normal level, he said: "I think better. He enjoys playing and training with his team mates. He is at a good level and without problems.
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"I think it is important now to put an end to the talking about Riyad. He has come back, he came in against Manchester City. Now we need to move on and for him, he has to kick on.
"He has come back with a smile. The story is behind him, all the players want to move on."
Puel said he will field a strong lineup when they host Sheffield United, who are currently eighth in the Championship (second-tier) standings.
"It will be a crucial game for us," he added. "I will pick a team to win the game, we want to get as far as we can in the FA Cup, of course. It will be a strong team like in the last rounds."
Japan forward Shinji Okazaki will miss the game due to a knee problem but Puel confirmed captain Wes Morgan could return to make his first appearance since picking up a hamstring injury in the 3-0 win over Huddersfield Town on New Year's Day.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
