The reports said foreign ministry spokeswoman Marzieh Afkham would be named ambassador to an Asian country.
Afkham herself said she could not comment on "rumours", quoted by state news agency IRNA. "Appointments at the ministry of foreign affairs are made after the necessary procedures."
In what was already a first for the Islamic republic, Afkham, a 30-year veteran of the ministry, was appointed spokeswoman in August 2013.
President Hassan Rouhani, who named two women as vice presidents, said Afkham's appointment was part of a "campaign to empower and elevate women in Iran."
But it was opposed by ultra-conservatives.
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The president's predecessor Mahmoud Ahmadinejad appointed a woman in 2009 as health minister before sacking her four years later.
He nominated several other women as ministers but they failed to win votes of confidence in Iran's conservative-dominated parliament.
Former reformist president Mohammad Khatami appointed Massoumeh Ebtekar in 1997 as vice president in charge of environmental protection, a post she retook under Rouhani.
She was the spokeswoman of radical Iranian students during the hostage-taking at the US embassy in 1979.
Although deemed more liberal than those of many Arab countries, Iran's laws since the revolution have been criticised as unfair to women in cases of marriage, divorce and inheritance.
While women may hold key posts, including in parliament and the cabinet, they can not serve as judges and have not been allowed to run for president.