Nasr-Azadani has played for a number of clubs including Persian Gulf Pro League team Tractor. He is said to have been arrested in November and accused of having a part in the killing of three members of the Islamic Revolutionary Guard Corps.
The IranWire website reported 26-year-old Nasr-Azadani is "in danger of execution" for an offence known as moharebeh, which is widely translated as meaning 'waging war against God'.
According to the website, Nasr-Azadani faces death by hanging.
Civil unrest and protests have been rife in Iran since a 22-year-old woman, Mahsa Amini, died in police custody in September after being arrested for not correctly wearing a headscarf.
FIFPro, which represents players worldwide, said it stood "in solidarity with" Nasr-Azadani.
It said in a statement: "FIFPRO is shocked and sickened by reports that professional footballer Amir Nasr-Azadani faces execution in Iran after campaigning for women’s rights and basic freedom in his country."
FIFPRO called "for the immediate removal of his punishment".
Former Iran and Bayern Munich striker Ali Karimi has also spoken out in support, denouncing the prospect of a death sentence and stating: "Do not execute Amir."