The Saudi owners of the Sirius Star are reportedly negotiating with pirate hijackers despite pleas from British and Saudi governments not to pay the ransom.
Chief engineer Peter French, from County Durham, and second officer James Grady, from Strathclyde are among 25 people being held on the ship.
Foreign Secretary David Miliband said payments were, "only an encouragement to further hostage-taking". His Saudi counterpart Prince Saud Al-Faisal said owners Vela International are in talks with the pirates.
"We do not like to negotiate with either terrorists or hijackers," but, he added: "The owners of the tanker are the final arbiters of what happens there."
A foreign news agency reported that the pirates have demanded 25 million dollars (£16.6 million) for the hostages' safe release. But Vela would not confirm this figure and maritime security experts said the true ransom is expected to be much higher.
A spokesman for the Foreign Office said British policy was not to negotiate with hijackers but conceded the Sirius Star, "is not a British ship".
"I cannot say if we have been contacted (by the pirates) or not. That is not something we can get into discussing," he said.
The UN approved a British proposal to impose new sanctions against Somalia in a bid to cut off the pirate gangs. It also called on the security council to recommend the freezing of assets of individuals and organisations.
The Sirius Star was attacked at the weekend 420 nautical miles off the coast of Somalia and the pirates who have taken control of the vessel have taken it to a stronghold near the town of Eyl. The 1,080ft (330m) long ship was fully laden with two million barrels of oil when pirates boarded it and is the largest vessel ever to be hijacked in a region which has become notorious for piracy.
Mr Miliband said he was "extremely concerned" about the situation and called on the international community to "stand firm" against hostage-taking in all its forms.
