The Daily Telegraph story said "reports have begun to circulate" about a possible cut in shipments through the Druzhba pipeline that feeds Poland and Germany, and that it was believed that executives from top producer LUKOIL had been put on notice.
"They have been told to be ready to cut off supplies as soon as Monday," The Daily Telegraph quoted "a high-level business source" as saying, without naming the source or describing how the source had access to the information.
The newspaper also said a senior Lukoil official in Moscow said he was unaware of any plans to curtail deliveries. It said the Kremlin declined to comment.
It also reported that the Polish government said Russian deliveries were still arriving smoothly and it was not aware of any move to limit supplies. The European Commission's energy directorate said it had received no warnings of retaliatory cuts.
Further comment was not immediately available.
Any move would be timed to coincide with an emergency EU summit in Brussels, where possible sanctions against Russia are on the agenda, the newspaper said.
Oil traders have watched with growing unease the escalating row between Russia and the West over Moscow's military action against Georgia, which initially disrupted some Caspian flows.
Moscow has defied pressure from the United States and European powers to pull out of Georgia.
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