Riyad Mahrez was still with Leicester when Deadline Day came to an end on Thursday night.
The forward had been given permission by Algeria to leave the national team's camp in order to complete a transfer but the day passed with no deal in place.
The Spanish window remains open for another 24 hours, though, so there is a chance Mahrez could still leave for a La Liga club.
In the early hours of Deadline Day, the Algerian Football Federation announced that Mahrez had permission to leave the Algeria squad and return to Europe to "formalise his transfer to his new club".
However, the Foxes have had no new bids for Mahrez, according to Sky sources, and the last offer they received was £31.8m from Roma over three weeks ago, which was still way below Leicester's valuation.
The Leicester winger had expressed a desire to leave the King Power Stadium and was linked with a host of clubs over the summer, Roma having had three bids rejected for the 26-year-old, the third being £32m.
Barcelona, Arsenal, Manchester United and Chelsea were also reported to be interested in Mahrez, who was PFA Player of the Year in 2016 after playing a key role in Leicester's shock Premier League title win that season.
Mahrez had been with the Algeria squad preparing for their upcoming World Cup qualifying double-header with Zambia, but the FAF gave him the green light to resolve his club future before the transfer deadline.
A statement on www.faf.dz read: "Leicester City's Algerian international Riyad Mahrez, who is currently with the national team in Sidi Moussa to prepare for the double confrontation against Zambia for the 2018 World Cup qualifiers, was authorised by the national coach Lucas Alcaraz and the Algerian Football Federation to make an express trip to Europe to formalise on Thursday his transfer to his new club.
"The national team will fly without him on Thursday morning to Lusaka to face Zambia on Saturday."