The agency is in discussions with Bacardi over the future advertising strategy and will use Jones for no more than one further commercial. The favourite to replace Jones is the Los Angeles-based actor Benicio Del Toro.
Del Toro, the star of 'The Usual Suspects', 'Snatch' and 'Traffic', is one of several names being considered by Bacardi, but insiders say a deal is close to being signed.
McCann has held the account for the entire Bacardi range since 1998, when it added the Bacardi Spice brand to its client list.
However, the agency's hold on the Bacardi Breezer business is under threat as the company is reviewing the £50m global account.
Jones appeared in his first spot for Bacardi in 2001, after he was drafted in by McCann to help make the brand's fiery Latin image more palatable for British drinkers.
He has since appeared in several commercials for the world's best-selling rum brand, the latest of which features him arm wrestling a young woman.
Del Toro is no stranger to advertising, having appeared last year in a series of cinema commercials for Mercedes. The campaign, which was entitled "lucky star", was created by Campbell Doyle Dye and BJK&E Media. Each commercial was designed to look like a movie trailer and contained no obvious branding.
A spokeswoman for Bacardi denied that Jones was being replaced. Jones' agent also denied the story.
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