Liverpool are monitoring a number of highly-rated youngsters across Europe, of which the Iranian striker is one of, as they consider boosting their attacking options in the January transfer window.
The 21-year-old joined Rostov in the summer on a two-year contract, after helping fire the Russian club to second place during his loan spell at the club last season.
Azmoun, who scored against Atletico Madrid in the Champions League earlier this month, is attracting interest from a number of top European sides.
Yet his representative, Mehdi Hagitali, claims Azmoun is focusing on his future with Rostov – citing the forward’s relationship with current manager Kurban Berdyev as a key factor.