Fekir was heavily linked with a move to the Gunners during the January transfer window, while Spanish champions Barcelona were also credited with an interest in the 24-year-old.
However, French outlet Football 365 reports that Arsenal's main competition for Fekir's signature will now come from AC Milan after Barca pulled out of the race due to already having too many players in his position.
The France international has directly contributed to 30 goals in just 37 appearances across all competitions this season, scoring 22 times and assisting another eight to help Lyon battle for second place in Ligue 1.
Arsenal are understood to have been quoted £60m for Fekir in January, but that asking price has since dropped significantly with Lyon now valuing the winger at closer to £35m.
However, Fekir is understood to favour a move to a Champions League club, which could scupper Arsenal's hopes should they fail to win the Europa League this season.