VTB is one of several Russian companies and individuals sanctioned by the West after Moscow's annexation of Crimea and its involvement in separatist rebels in eastern Ukraine.
The European Union will vote on whether to renew sanctions next month. Kostin said he hoped they could be "released" or eased. Those sanctions remain in place and the European Union has said that it is ready to reverse them once Russia "starts contributing actively and without ambiguities to finding a solution to the Ukrainian crisis."
Kostin added that the Russian state had expanded during the global financial crisis and that this should now be rolled back.
"The next step should be really a wide range privatisation," he told CNBC.
Among those companies Moscow is looking to privatize include oil giant Rosneft, diamond company Alrosa and airline Aeroflot, according to media reports. Like VTB, Rosneft is subject to international sanctions.
The Russian economy is set to shrink this year, but by less than in 2015 — the International Monetary Fund forecasts a contraction of 1.8 percent in 2016, versus 3.7 percent last year.
The country is grappling with a spiralling budget deficit and government departments have been told to cut spending by 10 percent this year, according to media reports.
In May, Russian Finance Minister Anton Siluanov said the deficit would come in at 3 percent of gross domestic product (GDP) in 2016, assuming oil prices averaged $40 per barrel, according to media reports. In 2015, Russia reported a deficit of 2.6 percent.
—With contribution from CNBC's Holly Ellyatt.