It is not clear whether the Algerian had permission to be absent.
City pulled out of talks for the 26-year-old on Wednesday after he made a transfer request the day before.
Foxes manager Claude Puel has confirmed Mahrez will not be considered for Saturday's match against Swansea, after missing the defeat at Everton.
"I hope Riyad can clear his head and come back with us as he is a valuable player for us and crucial in our play," Puel said on Friday.
City thought Leicester were asking for an overall package of £95m, which is said to have included striker Patrick Roberts, who is on loan at Celtic.
However, the Foxes would have accepted a straight £80m transfer for Mahrez, who has scored 35 goals and contributed 24 assists in 127 top-flight appearances - but that is still £20m higher than City's limit for the player.
He joined Leicester in January 2014 and was named the PFA Players' Player of the Year as the Foxes won the Premier League in 2016.
Puel said the club took the "best decision for our squad" and added that everyone involved now needs to "keep our focus on the pitch".
"We need to stay united after all this," he added. "It is a situation we need to manage but other things will stay inside the club. We will deal with his side and the club, not in public.
"All the players will help him to come back with positivity and a good mental attitude."
via Loud Naija Media
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