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The Saratov plant, which has a refining capacity of 6.8 million tonnes of oil a year, became part of Rosneft last year, after the company bought its peer TNK-BP for $55 billion.
It is one of a total 13 refineries owned by Rosneft in Russia.
Quoting sources, Kommersant said Rosneft was valuing the plant at around $400-$500 million and was in talks with a couple of players but had failed to reach any agreement so far.
Rosneft declined to comment. The company has asked the government for more than 2 trillion roubles ($43 billion) in financial support after it was put under Western sanctions over Moscow's role in the Ukraine crisis.
The measures limit its ability to raise funds in Europe and the United States.