Presidential spokesman Jeong Yeon-guk made the comments to reporters, without elaborating on the time frame for the possible visit.
Park, if the trip is made, would be the first South Korean president ever to visit Tehran.
South Korea is seeking to tap into business opportunities in Iran as the United Nations have lifted most economic sanctions against Iran in a follow-up to a nuclear deal reached with the US and five world powers.
Iran boasts the world's fourth-largest known crude oil deposits and ranks No. 1 in terms of natural gas reserves.
South Korea's exports to Iran reached US$4.14 billion in 2014, up 8.3 percent on-year. South Korea's share in Iran's imports, however, fell 0.5 percentage point over the cited period to 7.9 percent, according to data compiled by the state-run Korea Trade-Investment Promotion Agency.
