Arzani, who represented his country at the 2018 World Cup, is due to join Manchester City from Melbourne City before being sent on loan to Celtic for the 2018-19 campaign.
Rodgers has branded the 19-year-old "an exciting young talent", and is looking forward to welcoming the versatile attacker to Scotland.
"He is, I believe, finalising his deal with Manchester City and in talks with ourselves to come in, as a possibility," Rodgers told reporters. "He is another exciting young talent and we will see if we can get that organised in the next few days.
"It is not going to be [before] midweek. He has just flown in, he hasn't trained. He has obviously been at the World Cup so he will need to be in for a couple of weeks before he gets up to speed."
Arzani has scored twice in 26 first-team appearances for Melbourne City.