According to Interfax news agency on Thursday, the board had asked management not to declare bankruptcy of the oil group.
"The board's decision means that management must make all efforts to avoid the group's bankruptcy," the source said.
The Yukos board met last Friday to discuss the company's future, which has grown increasingly dark since it has found itself in the sights of the Russian authorities.
Yukos, whose imprisoned chief shareholder Mikhail Khodorkovsky is on trial for fraud and tax evasion, is locked in a desperate fight for its existence with the Kremlin in what observers say is revenge for the political ambitions of Russia's richest man.
Tax authorities have already demanded more than $7.5 billion in back taxes for 2000 and 2001 and the final bill could be significantly in excess of $10 billion.
Court bailiffs enforcing the tax demands have announced they will auction the main Yukos production subsidiary, Yuganskneftegaz, which accounts for 60% of Yukos's oil output.
Yukos, the largest Russian oil exporter which pumps one in five of every barrel of oil in Russia, has paid off more than $2 billion of the 2000 tax bill thanks to soaring world crude prices, but is in a losing race against time.