The 19-year-old also claims to have been approached by Serie A heavyweights Juventus and AC Milan after catching the eye in the Russian Premier League this season with three goals in 10 appearances.
He insists no decision on his future has been made as yet, with all options set to be considered.
The youngster is flattered by the interest, as he is yet to be capped at senior level by Iran, and has revealed that discussions regarding a possible summer switch will continue ahead of the re-opening of the transfer window.
Azmoun told showNavad: "I have offers from three major clubs: Arsenal, AC Milan and Juventus.
"I also had an offer from Barcelona, but due to their transfer ban the club is out of the picture at the moment.
"The talks with both Milan and Arsenal are getting very serious. Both clubs have spoken to Kazan.
"But for me, it's important to keep focus on Kazan. We have seven games left, I will decide after these games.
"I'm very proud to have Arsenal looking at me but, as I said, right now I'm only focusing on the Russian league."