Director of Minerals Phyl Rendell says one UK firm is ready to drill in 2007.
"But oil prices are now so high - the costs have gone up and you can't get a rig for love nor money."
A discovery would be important for long-term sustainability, but it could be 10 years before oil is found, she adds.
As for relations with Argentina, she says the oil "belongs to the Falklands" but a find would benefit both economies.
"The road will be rocky if there is a discovery."