'I hope for Riyad he can clear his head and he can come back with us because he's a valuable player for us, crucial in our play.
At a press conference, the 56-year-old told reporters: "The club took the decision for the best interest of Leicester, we needed to respect this decision".
Sky Sports News understands Mahrez has been left "depressed" by Leicester's decision not to accept City's final player-plus-cash offer worth an estimated £65m.
"We need to stay united after all this, it is a situation we need to manage but other things will stay inside the club".
It is understood that the 26-year-old Algeria worldwide is feeling so low that he is not in the right frame of mind to play. We will reassess Riyad when he clears his head. "It will be dealt with inside the club and not in public". "I hope he can come back quickly with us, and with a smile and happy to play with us".
'Even now, when Leicester look at the bigger picture, surely they will have to concede that Riyad Mahrez has been an unbelievably good player for them... but it's time to let him fulfil his potential'.
Puel insists there is a way back for the Algeria global, who played a starring role in Leicester's shock Premier League title triumph two years ago. It is important to move on and to keep our focus on the pitch.
'There is talk of him being fined for failing to show up for training, but I know - from personal experience - how galling it can be when your heart lies elsewhere in football.
"All the staff, especially all the squad, they are his friends".