"The minority shareholders have not exercised this right," Andrei Kazmin said.
The Sberbank supervisory board recommended Gref as the state-controlled saving bank's new president on October 16. Kazmin, who has held the job since 1996, will head Russia's postal service, to advance its modernization.
The former minister's candidacy is expected to be formally approved at a shareholders meeting on November 28.
His spokesperson earlier said that Gref had been considering a job in the business world after President Vladimir Putin reshuffled the Cabinet two months ago. A company was not named, but sources close to the former minister suggested it would probably be a state-run company.
An advocate of liberal economic reforms and Russia's economics minister from 2000, Gref earlier said: "A large bank is a conservative bank. If a bank keeps more than 50% of private individuals' savings nationally, it must be highly reliable. So there must be a focus on financial stability and a proper balance of its credit portfolio in terms of risks."
Gref also said he would focus on loans to small businesses, investment and plans to develop modern services like online banking.
Sberbank is the largest bank in Eastern Europe with assets totaling over 3.5 trillion rubles ($141 billion), or more than 25% of Russia's overall banking assets.
