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The Leicester winger has gone AWOL after the Foxes blocked his dream move to City last month.
The Blues tabled a deadline-day £60million bid which was knocked back by Claude Puel's side.
Leicester were apparently holding out for a figure closer to £90m but Pep Guardiola refused to budge in negotiations and the move fell through.
Mahrez has not turned up for training since the transfer window slammed shut and he is expected to push through a switch in the summer.
And the Daily Star say that Arsenal are hoping to tempt the Algerian to the Emirates Stadium.
The Gunners refreshed their squad last month by signing Henrikh Mkhitaryan and Pierre-Emerick Aubameyang.
However, Manchester United and Chelsea are also said to be closely monitoring the 26-year-old’s situation.
Arsenal boss Arsene Wenger has regularly made checks on the progress of Mahrez.
And if he cannot land Monaco star Thomas Lemar then Mahrez is seen as the best alternative.
Meanwhile, Leicester manager Puel thinks his attacker will return to the club in the near future.
He said: "After some time, he will come back with us.
"He is our friend and I think all the staff and all the players will help him to come back with a good mentality and a positive attitude and to enjoy his football with his team-mates.
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“Riyad is a good player but he is a good man also. I respect him. It's important to manage this with calm inside the club.
"We have a good relationship. (On Friday morning) I have seen my players with a good focus and with smiles and enjoying their training session.
"I hope there is a good solution.”
