Seven months after the U.S. deposed strongman Nicolás Maduro, Big Oil has yet to make any big moves in Venezuela. Exxon Mobil, Chevron and other major oil companies are fighting for a small number of the country's most attractive drilling spots, but some of the talks with Venezuelan leaders recently hit an impasse, according to people familiar with the negotiations.

President Trump and his lieutenants had high hopes that big U.S. oil companies would quickly sign investment deals to kick-start production in Venezuela, home to some of the world's largest reserves. They see the country's rising oil exports as a boon to U.S. supplies while Iran hobbles shipping lanes in the Middle East that typically carry 20% of the world's oil and gas.

The administration is also putting pressure on interim President Delcy Rodriguez to boost Venezuela's production quickly—before the end of Trump's second term.