A spokesman for Fortune declined to comment. But sources familiar with the situation said Fortune had discussed work on the offer with UK agencies.
Fortune has already appointed Credit Suisse First Boston as its financial adviser on the situation, but it is unclear whether it will hire a PR agency for a joint bid.
Fortune confirmed on 5 April that it was 'working closely with Pernod Ricard regarding its offer'. However, any appointment could depend on whether negotiations between Pernod and Allied come to fruition.
Sources said an Allied rejection of Pernod/Fortune's offer and a subsequent hostile bid would make additional PR support for Fortune more likely.
The possibility of a more protracted takeover battle for Allied increased this week after it emerged that rum maker Bacardi is also planning a bid.
Allied, whose brands include Ballantine's whisky, Beefeater gin and Courvoisier cognac, is using its retained agency of six years, Cardew Group, for financial communications.
Pernod, which in addition to its eponymous aniseed liquor owns Havana Club rum, has retained Citigate Dewe Rogerson for five years.
Pernod and Fortune are thought to be offering around 650p a share through a mostly cash offer made up with a minority of Pernod shares. This would give Allied a market capitalisation of £7.1bn and a break-up value of £8.9bn.
Privately owned Bacardi is said to be looking for a bidding partner to trump any agreement between Pernod, Fortune and Allied. The group has reportedly approached Jack Daniel's owner Brown-Forman in the US, and other drinks firms, for a possible £7bn joint bid.