The plan threatens to reignite a diplomatic row with Britain, which defeated Argentina 30 years ago in a dispute over who owned the islands, Britain's Daily Telegraph reported.
The president of Venezuela oil giant PDVSA, Rafael Ramirez Carreno, said last week he had met with officials of YPF to discuss exploration "in the territory and offshore areas, adjacent to the Falklands, but we have to analyze the costs and time."
The announcement on the anniversary of the Falklands war is the latest political swordplay between Argentina and Britain.
In June, the British government pledged to defend the islands, declaring there would be "no weakening" of the country's resolve.
Fifteen British and American banks advising companies exploring for oil around the Falklands received a letter from the Argentine government earlier this year threatening legal action.
Spanish firm Repsol claims its exploration rights in the Falklands have been "illegally expropriated" by YPF and warned of legal action against anyone doing business with the company.
Carreno said his company was "proceeding with caution."