The widespread Japanese daily Mainichi Shimbun said Abe would hold talks in Tehran with Supreme Leader Ali Khamenei and President Hasan Rohani.
Abe is due to arrive in Iran for a state visit between 12-14 June, during which he will meet with the two Iranian leaders, the newspaper quoted from government.
US President Donald Trump visited Japan last week and said he was open to talks with Tehran in what appeared to be a green light for the Japanese to act as mediators with the Iranians, according to the newspaper.
Prior to Trump's visit, Iranian Foreign Minister Mohammad Javad Zarif visited Tokyo in mid-May, and the official IRNA news agency mentioned that Zarif then discussed "the American measures and the tension that has provoked it."
Tensions between the United States and Iran have escalated since early May after the United States quickly sent the Abraham Lincoln aircrafts carrier and a series of B-52 strategic launchers and announced its intention to send 1,500 troops to the region to confront Iranian threats.
The Sultanate of Oman has entered the mediation line between Washington and Tehran, but the Sultanate has confirmed that Iran is ready to negotiate, but not in the current circumstances.