Abe is expected to make a final decision after consulting with US President Donald Trump, who is scheduled to arrive in Japan as a state guest on Saturday, the Kyodo News reported.
Abe would be the first sitting Japanese prime minister to visit Iran since Takeo Fukuda in 1978.
As Japan has traditionally maintained amicable ties with Iran, Abe hopes to encourage Tehran to keep its commitments under a 2015 international nuclear deal, according to the sources.
Abe expressed concern about the US-Iran standoff but offered to work with Tehran during a meeting with Iranian Foreign Minister Mohammad Javad Zarif in Tokyo last week.
The Japanese government weighed the possibility of Abe visiting Iran last summer but gave up on the idea out of consideration for Washington.
On Friday, Abe met with US National Security Adviser John Bolton at the prime minister's office and discussed the situation surrounding Iran, a Japanese government source said.
Tokyo, a longtime US security ally, has been put in a difficult position. The United States has ended its sanctions waivers granted to Japan and other buyers of Iranian oil. Iran has traditionally been one of the major oil exporters to resource-poor Japan.