"The Federal Tariff Service is expected to make a decision on the tariff in October, the rise would be within inflation - around 6 percent," Barkov told reporters.
The tariffs are Transneft's only source of revenue and an important item in the cost line for oil companies.
Barkov also said that expansion of the Caspian Pipeline Consortium (CPC) project, 31 percent owned by Transneft, could be delayed by six to 12 months.
"The expansion may be delayed for a number of reasons, including for the reason that Kazakhstan's (oil) reserves turned out not that sizeable," he said.
CPC plans to expand annual capacity of the pipeline, which connects Kazakhstan's Caspian Sea oil deposits with the Black Sea port of Novorossiisk, to 67 million tonnes from 30 million tonnes.
Transneft, which runs Russia's 50,000 kilometre-long network of oil pipelines, is on the Russian government's list of the companies it wants to part-privatise.
Last year, Russia's Economy Ministry suggested selling a 3 percent voting stake in Transneft, in a proposal backed by Prime Minister Dmitry Medvedev, who was then president.