Analysts have valued Stolichnaya at $3bn (£1.54bn) and say an auction is likely to attract many large global spirits groups that currently do not have a leading vodka brand in their portfolio.
Possible suitors for the brand may include Brown Forman, which owns Southern Comfort, Bacardi-Martini and Campari.
A sale process is expected to begin within the next few weeks and SPI's options include either a full sale of the brand or the sale of its international distribution rights.
SPI has been licensing the distribution rights outside Russia to the French group Pernod Ricard. However, Pernod has had to give up its rights after it gained Swedish vodka brand Absolut through its $8.1bn purchase in April of Vin & Sprit from the Swedish government.
Pernod had previously held talks with SPI about acquiring the Russian rights to Stolichnaya, but was not allowed to own both vodka brands for antitrust reasons.
In April, Stolichnaya called a review of its global advertising account. A representative for SPI contacted London agencies with a view to putting together a longlist to pitch for the business.
The winning agency was expected to create a campaign that moved away from its current advertising strategy, which is based around Soviet-style themes, and instead focus on more contemporary communications.