Benzia is on a season-long loan in Turkey from French club Lille.
While the 24-year-old is not on Fenerbahce’s list for the league he is in their Europa League squad.
He played 13 Super Lig games in the first half the season but is now left struggling for playing opportunities ahead of the Africa Cup of Nations.
His most recent appearance was in the club’s 2-0 win over visiting Goztepe on 1 February.
According to Fifa regulations he is unable to return to parent club Lille outside the transfer window.
Fifa’s regulations also prevent players for playing for more than two different clubs in the same season.
With Benzia having played for both Lille and Fenerbahce so far this season his options to play seem limited to joining a club whose season begins in the coming months such as China or MLS in the USA.
The Fifa transfer regulations state that “A player is only allowed to be registered with a maximum of three clubs in one season but the player is only eligible to play official matches for two clubs.”
“However, a player may be eligible to play in official matches for a third club during the relevant season if he has moved between two clubs belonging to associations with overlapping seasons (ie, start of the season in summer/autumn as opposed to winter/spring).”
In order for such a move, both Lille and Fenerbahce would have to agree to a deal.
Benzia played for France at youth level, featuring at the 2011 Under-17 World Cup in Mexico, before switching allegiance to Algeria.