The 19-year-old says he has received offers from both clubs, whilst Italian giants Juventus have also been linked, having scored three goals in 10 appearances this season.
The forward insists he has not made a decision on his future, and is still considering all options.
“I have offers from three major clubs: Arsenal, AC Milan and Juventus,” Azmoun said.
“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.”
Azmoun joined the Russian club from Iranian outfit Sepahan in January 2013.
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