The agency was briefed, through ISBA, alongside Abbott Mead Vickers BBDO and Rainey Kelly Campbell Roalfe/Y&R to deliver a strategic proposition, which would bolster the brand's presence in the UK.
AMV and RKCR/Y&R have been informed that they are no longer in the running for the business, although Fallon's appointment has yet to be ratified by the wine-maker's head office.
Jacob's Creek, which spends £4 million in the UK, is considering what its next move should be following the completion of its Friends sponsorship when the series ended.
The brand launched its "say when" campaign when it replaced Nescafe as the sponsor of the US sitcom in 2002.
Clemenger BBDO in Adelaide produced the creative work for the idents, which played on the association of drinking wine and friendship.
Jacob's Creek will continue in its role as the official wine supplier to the Wimbledon tennis championships, supporting the tournament through press and poster ads, as well as a sampling campaign targeting more than one million consumers.
But the brand is interested in raising its television profile through alternative sponsorship deals.
A survey conducted by SPA, the independent research company, revealed more than one-third of viewers were more likely to buy Jacob's Creek following the brand's sponsorship of Friends.
The consultation follows the arrival of Rachel Gristwood as the brand manager for Jacob's Creek earlier this year and a revamp of its packaging.
Jacob's Creek's sales have grown by 24 per cent over the past five years, during which time Australia has become the largest exporter of wine, outside the European Union.