The sale, worth about $5 billion based on market prices, is part of a wider state privatization drive that was initially scheduled for last year but has been repeatedly delayed due to fragile markets.
Kommersant, citing sources, said Tuesday that state-controlled Sberbank restarted talks with investors late last week and could open an order book this week, encouraged by a recovery in financial markets.
Two sources close to the placement said that while Sberbank is ready to launch the secondary share offering, it has yet to make a final decision on timing.
"There is no decision yet," one of the sources said, adding that once a decision is made, the road show can start at any time.
The sale would bring the free float in the bank to 50 percent and leave the state in control.
Shares in Sberbank, which last month posted better-than-expected second-quarter profit, have risen about 17 percent this year, outpacing the broader MICEX index, which is up 5 percent.
"The final decision on placement will probably be made only after it becomes clearer whether markets are to remain favorable," said Natalia Berezina, an analyst at UralSib.