Roster agencies Design Bridge, Williams Murray Hamm and Pearlfisher are battling for the task to modernise the brand.
The company has insisted on keeping the grouse as an integral part of the packaging, which was last overhauled five years ago.
The makeover is expected to be evolutionary rather than radical, but may involve a revamped bottle shape as well as different graphics.
The blended malt was first produced by Matthew Gloag in 1896 under the name Grouse Brand; his daughter Phillippa drew the first red grouse for the label. Two years later, the whisky had become so popular that the word 'famous' was added to the moniker. The Famous Grouse has been Scotland's bestselling blended malt for more than 20 years.
It sits at number two behind Bell's in the wider UK market with 16.3% value share, according to Mintel.
However, it is gaining on the market leader, which has 19.8%, according to global marketing manager Murray Calder.
Last year, Edrington opened a £2.5m visitor centre for the brand at its oldest working distillery in Glenturret, to capitalise on the growth of "whisky tourism" in Scotland.
The Famous Grouse Experience is based on the ads created by Abbott Mead Vickers BBDO since 1996, and teaches visitors about "nosing" as well as ad production.
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