The reports emerge as Prime Minister Narendra Modi is likely to visit the oil-rich country later in May.
"We are working on clearing the dues to Iran and are hopeful that the issue will be resolved soon," the NDTV broadcaster quoted its sources as saying.
According to the broadcaster, a series of bilateral negotiations at various levels has been held both in Tehran and New Delhi. The sources reportedly told the media that both sides were confident of being able to soon resolve the issue.
However, according to the media, despite the Western sanctions imposed on Iran now being lifted, there are still some issues with the banking channels which create obstacles for regular transactions.
In mid-January, the sanctions were removed after the International Atomic Energy Agency verified Tehran’s compliance to the nuclear agreement.
Following lifting of sanctions, Iran terminated the discounts for India, which included the payments being carried out in rupees, and free delivery of oil, and has since been insisting on payments for the crude it exports to Indian refineries to be carried out in euros.