Arzani, 19, has lit up the A-League this season, with his scintillating attacking displays for City, prompting calls for his inclusion in the Australia squad for the 2018 FIFA World Cup.
However, the teenager is also eligible to represent Iran - his country of birth - causing his international future to become a hot topic.
Arzani has played for Australia at Under-17, U20 and U23 levels, but has never been capped as a senior international.
And now Iran coach Queiroz, whose side will also be at Russia 2018, told FOX Sports Asia he and his staff know all about the attacker and monitor him closely.
"We follow with all the details all national team players," Queiroz said.
"And with the player you mentioned (Arzani) - we've been following him very closely, with full details of every single game.
"We have direct observations and analysis, and video analysis, of every single game of all national team players and he is part of our system.
"We've been watching very closely, we've been analysing all the games he's been playing. We have deep research and analysis on him, and all the other players.
"In the end, the decision will be made on the capabilities and skills and character of each player to be part of the national team."
The Portuguese coach also said, however, that he would 'never' cap Arzani simply to lock him down for Iran.
"In my long experience with international football players, especially the players that have the possibility to choose which national team they can play. I never challenge one player to play with the national team that I’m working for if I’m not sure that he has the real possibility to have an impact on the success of the team," he said.
"It has happened with other Portuguese players that they call them to other national teams to stop them playing for Portugal, and I've always thought that was not a good move, not a correct and honest move.
"So I will never do that with other players, because I'll feel bad personally if I challenge a player to play for Iran, and after me or any coach stops coaching the team.
"This decision is very complex and it's a big decision and we can only take this decision if we are absolutely sure that this player will have a huge impact with the national team of Iran.
“I don’t want to go into full details because I don’t do that for any other player.
“But of course, it's obvious that if we are following him game after game it's because we recognise he's a player with good potential."
Arzani himself, has expressed a preference for the Socceroos over Iran, without overly committing himself, and said in February: "I am leaning a bit more towards Australia".
"I grew up here, I played all my football here and went to the AIS. I have a lot of memories here.
"I'd be very happy to get called up (to the Socceroos) and I feel like I'm as ready as I'll ever be.
"I think I can be a bit better physically but my mindset is as good as it's going to get."
Iran are in Group B at the World Cup with Spain, Portugal and Morocco.