The US-based company has held meetings with agencies, including UK shops, interested in pitching for the business.
Brown-Forman is expected to task the winning agency with initial work on the global strategy and creative for Maximus Vodka, the Polish brand that was acquired in June last year.
There is also an opportunity to work on Finlandia Vodka, which was acquired by Brown-Forman in 2004.
In the past, Brown-Forman has worked with Iris on Finlandia. The agency created a summer campaign for the brand in 2008 that aimed to communicate its "natural purity". The UK activity spanned outdoor, online, print, experiential and PR, and included a takeover of Euston station in London, with Finlandia wraps on the corridors and escalators.
Brown-Forman's other alcohol brands include Jack Daniel's Tennessee Whiskey, Southern Comfort, Canadian Mist and Woodford Reserve bourbon.
Brown-Forman plans to push Maximus in markets outside of Poland after acquiring the brand from the Finland-based Altia for an undisclosed sum.
Previous Maximus ad campaigns include a 2008 spot with the strapline: "Maximus: see where it takes you."