Fekir, 24, has been linked with a possible move to The Emirates in the past and a switch to Arsenal would see him link up with his former Lyon team-mate Alexandre Lacazette.
The attacker has been in top form for Lyon so far this season, having scored 11 goals and made four assists in 14 Ligue 1 games for Lyon this term.
And he has left the door open for a potential move to the Premier League by naming both Arsenal and Manchester United as possible destinations.
Asked about his favourite leagues, Fekir told French media outlet Telefoot: “Spain, with Real [Madrid], Barcelona & Atletico [Madrid] who are the big clubs.
“After that there is England: Manchester United, Manchester City, Arsenal. I don’t have a specific club [I want to go to].
“Is this my last season at Lyon? I don’t know what the future holds for me. I’ve still got two years left on my contract. So, I’m still Lyonnais.”
Both Arsenal and Manchester United are likely to be keen to want to bolster their squads in the January transfer window as they look to try and close the gap to high-flying Manchester City at the top of the table.
Arsenal will return to Premier League action on Friday night when they take on Liverpool FC in a crunch top-four clash at The Emirates in their final game before Christmas.
The Gunners finished fifth in the Premier League last season.
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