The 19-year-old joined the Russian side on a free transfer from Iran Pro League side Senaphan in January 2013. Azmoun has since made 10 appearances for the club, scoring three goals - including two in Rubin's last two matches against Zenit St Petersburg and Rostov.
Recent reports have suggested Arsenal have made a £2 million bid for the Iran Under-20 international, and Azmoun has revealed talks between the two parties are set to take place.
"There already are solid offers coming from both Arsenal and AC Milan," said the Iranian. "Both their representatives are about to meet Rubin Kazan management next Thursday.
"I'm really happy for such clubs being interested in signing me, and playing in Premier League would be a dream come true.
"But now I'm just focused on the remaining part of Russian championship."
Azmoun has recently broken into Rubin Kazan's first team, and started in the Russian outfit's last four matches.
