Earlier this summer the 26-year-old handed in a transfer request to force a move away from the King Power and has since been the subject of three failed bids from Serie A side Roma, who have fallen short of the Foxes' £50m valuation.
Mahrez is currently on international duty with Algeria ahead of their World Cup qualifier with Zambia on Saturday, but in a statement issued overnight, the country's FA confirmed that he has been given temporary leave to sort out his club future.
"Leicester City FC's Algerian international Riyad Mahrez, who is currently with the national team in Sidi-Moussa preparing for the games against Zambia in the 2018 World Cup qualifiers, was authorised by national coach Lucas Alcaraz and the Algerian Football Federation to make an express trip to Europe to formalise his transfer to his new club on Thursday," it said.
"On Thursday morning the squad will fly without him to Lusaka to face Zambia on Saturday at 15:00 local time (14:00 Algerian time)."
Arsenal have been previously linked with Mahrez and could now return for him, with Alex Oxlade-Chamberlain's departure for Liverpool expected to be confirmed today, while Manchester United have also been rumoured to make a late bid.