The U.S.-bound Sirius Star, owned by Saudi Aramco, was seized on Sunday about 830 km (516 miles) southeast of Mombasa, Kenya.
The Okaz newspaper said, citing a source in the Saudi border guard service, that the option of force could not be ruled out "in the future." The source also said that Saudi authorities were also studying ways of providing security for oil tankers and other cargo ships.
The pirates have demanded $25 million for the release of the Sirius Star and its crew, and insist that the ransom be paid within the next 10 days.
The South Korean-made 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.
The crew includes citizens of Croatia, Britain, the Philippines, Poland and Saudi Arabia.
Somali pirates have attacked around 83 ships so far this year, resulting in the seizure of around 33 vessels, including 200 crew members. The East African nation has been without a functioning government since 1991.
The Russian frigate Neustrashimy (Fearless) recently joined an international naval group that has surrounded a Ukrainian ship, the MV Faina, seized by Somali pirates on September 25. The Faina's Russian captain died of a heart attack after the vessel was seized.