The 24-year-old moved to Zenit from Rubin Kazan on 1 February this year and has been finding the back of the net on a regular basis ever since.
Azmoun has scored 14 goals in 17 matches across all competitions since his arrival, including two in the Russian Super Cup on Saturday, which Liverpool scouts were in attendance for, according to SovSport.
Zenit went on to lose 3-2 to Lokomotiv Moscow, but the brace from the Iranian appeared to confirm to the visitors from Merseyside that he is the bright talent they thought he was.
Liverpool were first linked with Azmoun back in the January transfer window of 2017, but he was not interested in the switch due to a likely lack of game time.