Fekir has emerged as one of Ligue 1's outstanding talents this season, having already matched his goal tally of last season to help fill the void left by Alexandre Lacazette, who joined the Gunners for a club record fee during the summer transfer window.
The attacking midfielder, thriving once again after missing most of the 2015-16 season after tearing knee ligaments, has been tipped as a possible replacement for Mesut Ozil at the Emirates, with the Germany international looking increasingly likely to leave the club when his contract expires at the end of the season.
But the 24-year-old, a former teammate of Anthony Martial at Lyon, has also described United as "a club that makes you dream", with Real Madrid boss Zinedine Zidane also said to be a huge admirer of a player who is Barcelona's alternative option to signing Philippe Coutinho, according to reports in Spain.
Fekir's current contract at Les Gones expires in 2019, with the likelihood of a big-money move increasing every day. For now, he is solely focused on Lyon, but has a host of Premier League and La Liga clubs on his mind.
"There's nothing concrete with Barcelona," Fekir told Telefoot. "Spain makes me dream: Real Madrid, Barcelona, Atletico Madrid. Those are great clubs.
"But there is also England, with Manchester United, Manchester City and Arsenal. 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."
Fekir, who has 14 goals and three assists from 21 appearances this term, isn't likely to move on until next summer, however, with Lyon's president Jean Michel-Aulas insistent there is no possibility of a January exit.
"Of course [he will stay in January], and nothing says he'll leave at the end of the season," Aulas told SFR Sport in November. "He's under contract, he's happy in Lyon.
"He's enjoying a period of success football-wise, but also in terms of management as he's captain of an Olympique Lyonnais that has been able to get itself back on track, and it's also thanks to him."