"Negotiators on behalf of the owners of the Sirius Star have agreed to pay the ransom," the Okaz newspaper quoted one Abu Bakr Dary as saying.
He also told the paper that the supertanker and its 25 crewmembers would be released within 72 hours of the ransom being received.
The pirates initially demanded $25 million dollars for the release of the vessel. There have been unconfirmed reports that they have now agreed on around half this sum.
The crew of 25 includes nationals from Croatia, Britain, Philippines, Poland and Saudi Arabia.
Saudi Foreign Ministry spokesman Khalid bin Saud bin Khalid said on December 1 that the Saudi authorities were not in negotiations with the pirates and did not intend to pay a ransom.
The Liberian-flagged oil tanker MV Sirius Star, owned by Saudi Aramco, was seized about 830 km (516 miles) southeast of Mombasa, Kenya on November 15.
The supertanker is believed to be carrying some 2 million barrels of crude, equivalent to a quarter of Saudi Arabia's daily output. It is the largest ship ever captured at sea.
Somali pirates have attacked around 90 ships so far this year, resulting in the seizure of around 39 vessels, including 200 crew members. The east African nation has been without a functioning government since 1991.
UN Secretary-General Ban Ki-moon said in his quarterly report to the UN Security Council in November that pirates had earned up to $30 million in ransoms this year.
