By Alexandra Ulmer and Marianna Parraga

CARACAS/HOUSTON, March 16 (Reuters) - Venezuelan state oil company PDVSA has offered Russian counterpart Rosneft a stake in a joint venture in the country's Orinoco Belt extra-heavy crude area, five industry sources said, in a sign of the Latin American nation's dire economic situation and Moscow's growing muscle there.

Rosneft, Russia's top oil producer, has been offered a 10 percent stake in the Petropiar joint venture. PDVSA has a 70 percent share, and U.S. oil company Chevron Corp holds 30 percent of the venture, which includes an oil field and a 210,000 barrel-per-day oil upgrader.

Two sources said the offer was part of a larger package put to Rosneft as PDVSA seeks to raise money for major debts with providers and bond payments.

It is unclear if Rosneft will accept the offer. Financial details of the potential transaction were not immediately available.

PDVSA and Venezuela's Oil Ministry did not respond to requests for comments. Chevron and Rosneft declined to comment.

A deal would have California-based Chevron working alongside state-owned Rosneft, which has been affected by U.S. sanctions against Russia. But Chevron's main concern is that accounting and transparency laws are less strict in Russia than in the United States, a source close to the matter said.

The proposal highlights Venezuela's need for cash after the nation's oil output fell about 10 percent last year, according to the Organization of the Petroleum Exporting Countries. This has worsened a recession that has millions of Venezuelans skipping meals.

MOSCOW'S MUSCLE

Rosneft has already been gaining ground in Venezuela, an OPEC member.

Last year, the company paid $500 million to increase its stake in the Petromonagas joint venture from 16.7 percent to 40 percent, the maximum foreign partners are allowed to have under oil sector regulations created under late leader Hugo Chavez.

That raised the ire of the opposition-led National Assembly, which said the purchase was illegal because Congress did not approve it. Critics have also said the stake was sold too cheaply.

In another controversial move, PDVSA last year used 49.9 percent of its shares in coveted U.S. subsidiary Citgo as collateral for loan financing from Rosneft. PDVSA said this month it had received $1.985 billion from an unnamed client in return for future oil shipments, with Citgo shares used as a guarantee.

In total, Rosneft has lent PDVSA between $4 billion and $5 billion, but the details of those deals have not been disclosed.

"We must thank life that Russia and the world have a Vladimir Putin," Venezuelan President Nicolas Maduro said at a deal-signing event with Rosneft head Igor Sechin last year.

"I wanted to be here at this event because of how important relations with the new Russia are." (Additional reporting by Ekaterina Golubkova and Vladimir Soldatkin in Moscow; Writing by Alexandra Ulmer; Editing by Christian Plumb and Lisa Von Ahn)