Saudi Arabia, the United Arab Emirates, Bahrain, Egypt and Yemen were among those to cut ties with Qatar on the grounds that Doha supported extremist groups "that aim to destabilise the region".
The rift has triggered the closure of air space and the expulsion of diplomats.
It also means a new venue will have to be found for the matches between the two teams, scheduled for August and September.
John said the new neutral venue could be identified over the next two weeks. Neither Saudi Arabia nor Iran play matches at home.
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Persepolis spokesman Pendar Khomarlou told AFP the team was unaffected by the Gulf diplomatic bust-up, the biggest to hit the region in years.
"Saudi and Qatar have political problems. Saudi may choose Abu Dhabi. We have no problems with playing in Abu Dhabi since we have a lot of supporters living there," he said.
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