A conservative, Hashemi-Rafsanjani is currently the chairman of the Expediency Council, the country's top political-arbitration body.
Serving as president and Expediency Council chairman simultaneously could make Hashemi-Rafsanjani the country's most powerful official.
Hashemi-Rafsanjani served two terms as president (1989-97) and has consistently denied any interest in serving again, citing a preference for seeing new faces at the country's helm.
He said the current problem lies with the weak parties that do a poor job of promoting candidates.
Hashemi-Rafsanjani withdrew from the February 2000 parliamentary race after it appeared that he would not be among the top 30 finishers in Tehran, Radio Farda reported.
Radio Farda suggested that Supreme Leader Ayatollah Ali Khamenei would only approve of another Hashemi-Rafsanjani presidency if neither of his preferred candidates -- Ali Larijani or Ali Akbar Velayati -- has a chance.
The presidential balloting is slated for 17 June.