The Rubin Kazan striker had been linked with English clubs but the 23-year-old player had said he will choose his next club after the 2018 World Cup.
The Scottish Sun has reported that Azmoun is a target of Celtic and there is a possible move in the summer.
The Scottish club is also reportedly want to sign Ostersund striker Saman Ghoddos.
Ghoddos, 24, has hit 31 goals in 70 games for the Swedish club since signing from Syrianska, and after notching two assists against Arsenal on Thursday, Celtic has shown interest in signing him.