The North African country revealed the news via their Twitter account early on Thursday morning, with the deadline rapidly approaching.
Mahrez, valued at £50million by Leicester, was currently training with his international team-mates ahead of a World Cup qualifier against Zambia on Saturday.
“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.
“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),” the Algerian Football Association said in a statement.
Mahrez had been linked with Roma in the early part of the summer window but that deal appeared to have gone dead. The Serie A club saw three separate approaches for the player turned down by Leicester.
Also, Spanish newspaper AS reports that Barcelona have informed Mahrez that he is their back-up option should their move for Philippe Coutinho fail to go through.