Bacardi Martini has also shortlisted Campbell Doyle Dye and Quiet Storm to complete the four-strong list.
The company revealed last month that it was ending its relationship with McCann Erickson after 10 years, following a period of tension between agency and client.
The two parties had been in talks for several months to try to find an alternative strategy to its "Welcome to the Latin Quarter" creative, but the ideas that were presented by McCanns were rejected, and the relationship came to an end.
In its most recent results, Bacardi saw net profits decline by 21% to $331m (拢171.5m), and chief executive and president, Javier Ferran, resigned from the company in November.
McCann's most recent work for Bacardi was "platform", featuring the actor Raoul Bova. It succeeded a long-running campaign starring Vinnie Jones.
Both campaigns used the "Welcome to the Latin Quarter" theme. However, new regulations drawn up by Ofcom will clamp down on advertising for drinks brands that associates drinking with partying and excessive behaviour. The restrictions will form part of the government's crackdown on binge drinking.
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