CARACAS, Venezuela—The Venezuelan government is investigating alleged corruption in a $1.3 billion contract between the state oil company and a private contractor co-founded by a Saudi prince, according to law-enforcement officials and related documents.

Venezuela’s inspector general’s office on March 6 recommended that the Public Prosecutor’s Office investigate and charge five current and former executives at Petróleos de Venezuela SA, or PdVSA, for allegedly embezzling public funds by paying inflated fees for the lease of an oil rig, according to a copy of the request seen by The Wall Street Journal.

The rig, the PetroSaudi Saturn, was the second drillship leased by PdVSA from PetroSaudi International Ltd. to develop natural-gas reserves that the Venezuelan company said would make the country a global gas superpower.

The entire offshore project, Mariscal Sucre, has yet to produce any gas. “Mariscal Sucre is PdVSA’s eternal white elephant,” said Antero Alvarado, Caracas-based analyst at consultancy GasEnergy Latin America. “They sank billions on it with nothing to show for it.”

A PdVSA spokesman declined to comment on the contracts with PetroSaudi, citing legal disputes between the two companies.