Iran's state-run IRNA news agency on Friday quoted Iranian soccer federation spokesman Amir-Mahdi Alavi as saying that officials faced visa obstacles that go beyond sports considerations.
There was no immediate comment from the White House.
Alavi said the federation had reached out to FIFA and hoped it could help resolve the issue.
President Donald Trump's administration announced in June a travel ban on citizens from 12 countries including Iran. The list also included Haiti, who also qualified last week for the World Cup finals to be staged in the US, Mexico and Canada.
Exemptions, however, were promised for "any athlete or member of an athletic team, including coaches, persons performing a necessary support role, and immediate relatives, travelling for the World Cup, Olympics, or other major sporting event as determined by the secretary of state."
It is unclear whether the exemptions also apply to the World Cup draw, which takes place on December 5 at the Kennedy Center.
The Iranian delegation would have been expected to be led by its soccer federation president Mehdi Taj, one of the most senior officials in Asian soccer and a member of two FIFA committees that oversee the World Cup.
He is one of the vice-presidents of the Asian Football Confederation and a member of FIFA panels with responsibility for the ruling body's competitions, plus men's national team soccer in general.
A record 48 teams will participate in the World Cup between June 11 to July 19.
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