Edelman, which was appointed in 2010 following a pitch against Portland, Hanover and Blue Rubicon, is repitching for the account.
PRWeek understands that FleishmanHillard is also in the running for the work. It is unknown how many other agencies are pitching.
An agency is expected to be appointed in the next month. The process is being led by Becky Perry, head of comms at Diageo GB, and Rachael Robertson, head of public affairs.
Drinks giant Diageo owns Smirnoff Vodka, Guinness and Baileys.
The agency list is closed.