The spokesman for Heinz Fischer says the Austrian president has been invited to Iran.
If he accepts the offer, Fischer would become the first Western head of state to visit the Islamic republic since President Hassan Rohani took office last August.
Rohani, who is regarded as a moderate cleric in Iran's Islamic system, has promised to improve Tehran's ties with the international community.
In recent weeks, several high-ranking foreign officials including, Turkish Prime Minister Recep Tayyip Erdogan and Swedish Foreign Minister Carl Bildt, have visited Tehran for talks with Iranian leaders.
The Austrian capital, Vienna, is currently hosting talks between representatives of Iran and six world powers aimed at reaching a long-term deal that would resolve concerns that Iran is trying to make a nuclear weapon.
Iran denies any such effort.
Based on reporting by AFP and Reuters