The office of TNK-BP has been searched twice by Russian police.
The head of BP's oil venture in Russia is to be quizzed by Moscow as part of a tax evasion probe, reports say.
The Interior Ministry has issued a summons to TNK-BP chief executive Robert Dudley, according to the Financial Times and Reuters.
The development comes amid speculation that a state-controlled firm will try to buy a slice of TNK-BP.
Last month Russia's security services raided BP's Moscow headquarters - for the second time in two months.
That raid was reported to be linked to the firm's involvement with Gazprom.
Reuters reported that the tax evasion probe may relate to TNK - the non-BP side of the business - which Mr Dudley has never worked for.
Foreign energy companies have come under increasing pressure in Russia as the government has been trying to increase its control over oil and gas assets.
TNK-BP was told last year that it was in danger of losing its production licence for a Siberian gas field for not meeting production targets.
The company eventually sold its stake in the Kovykta field to Russian state-controlled Gazprom.
Also last year, Royal Dutch Shell was forced to hand over part of its stake in a massive Siberian gas field.