And the 21-year-old forward could make history if he signs on at Anfield.
No Iranian players have ever played for Liverpool - and he could become the first one in the clubs history.
However, Iran has already been represented in the top flight.
Karim Bagheri became the first when he made his debut in England for Charlton - although the spell ended after he played just 15 minutes all season.
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Sardar Azmoun is just one of a number of players that Liverpool have been watching[/caption][caption id="" align="alignnone" width="620"]
Sardar Azmoun has played for the Iranian international youth sides[/caption]Andranik Teymourian since turned out for Bolton before Ashkan Dejagah became No.3 for Fulham.
Azmoun, 21, has caught the eye with a series of impressive displays for Russian outfit Rostov.
He is just one of a number of players that Liverpool have been watching recently.
The Iranian is a versatile player that can play in a number of positions behind the main forward.
There is no indication that Liverpool will move for him any time soon but he the club are giving him a thorough watch.
Liverpools expected line-up to face Bournemouth
Friday, 2nd December 2016
LIVERPOOL take on Bournemouth on Sunday, but who will make the starting line-up?
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LIVERPOOL FC[/caption]Liverpool (Odds: 8/11 to win, 3/1 to draw, 7/2 to lose)
Even if they did swoop January, he is not the sort of player that will suddenly add something different to what they already have.
He is one that would grow into the club and become a more prominent figure as time goes by.
Much like how Marko Grujic, signed last January before being loaned out for the rest of the season, is being dealt with in his debut campaign at the club.
When asked about a potential move away from Rostov, he said: "Ajax, PSV or Liverpool? I have not received any offers.
If there are, then Im going to take my time to look into it, whether its come from Liverpool or other clubs.
