The Gunners are understood to have been tracking Fekir for some time now, but a rumoured move to the Emirates Stadium in January failed to materialise as Arsenal instead signed Pierre-Emerick Aubameyang.
However, Arsenal have retained their interest in the 24-year-old, and L'Equipe reports that they have been handed a boost in their pursuit of the player after Lyon informed him that he would be allowed to leave this summer.
The agreement is reportedly part of Fekir's contract at the club - which runs until 2020 - meaning that he would be free to find a new team if a suitable offer arrives, even if Lyon qualify for next season's Champions League.
Arsenal are expected to face competition from AC Milan for the France international's signature, and Lyon are unlikely to consider any offers below £35m for their star man.
Fekir has scored 22 goals and created eight more across all competitions this season.