Iran's football federation (FFIRI) has been pushing to move the team's three World Cup group-stage matches from the United States to Mexico, citing American military involvement alongside Israel in strikes that sparked an ongoing war in the region.
FFIRI said last month they were in discussions with FIFA about a venue switch, while Iran's sports ministry has banned national and club sports teams from travelling to countries it considers hostile until further notice.
FIFA president Gianni Infantino said last week, however, that Iran would play their matches as scheduled.
"Our request to FIFA to relocate Iran's games from the U.S. to Mexico is still valid, but we have not yet received a response," Donyamali told Turkish state news agency Anadolu in an interview published at the weekend.
"If accepted, Iran's participation in the World Cup will be certain. However, FIFA has not yet responded.
"As the Minister of Sports, together with the Iranian football federation, we will keep the football team ready for the World Cup. However, the final decision will be made by our government."
Iran are scheduled to play all of their Group G matches on American soil - against New Zealand and Belgium in Los Angeles before their final fixture against Egypt in Seattle.
US President Donald Trump said last month that while Iran's national team were welcome to play in the U.S., it might not be appropriate for their "life and safety".
He later made it clear that any threat to players would not come from the United States.
"According to FIFA's relevant regulations, security must be provided in the country concerned," Donyamali added. "However, the World Cup is taking place soon, and providing guarantees during this period is questionable.
"Under these circumstances, the possibility of Iran participating in the World Cup matches in the U.S. is very low. But, if the relevant security guarantees are provided, our government will make the decision on Iran's participation in the World Cup."
FIFA did not immediately respond to an emailed request for comment.
The World Cup takes place in the US, Mexico and Canada from June 11 to July 19.