The brand, which currently creates its advertising in-house, is owned by the Swiss luxury goods group Richemont.
A spokesman confirmed that the agency is in exploratory talks with agencies but said that it had not yet reached the pitch stage.
Hackett has a unique positioning, which attracts traditional customers, for its stock of tweeds and top hats, while also appealing to a younger, more streetwise audience.
Its latest ad campaign featured the England rugby star Jonny Wilkinson, kicking a rugby ball while wearing a tweed jacket.
The discussions on the creative account do not affect the brand's media agency, Mediaedge:cia, which handles the media across Richemont's portfolio of brands.
Up until 2000, Hackett retained Hudson Wright Associates as its creative agency. It then embarked on a hunt through the AAR for an agency to launch a £3 million campaign to revitalise the brand in the UK before abandoning the pitch on the orders of its owners.
Separately, the Richemont-owned Alfred Dunhill brand is looking for an above-the-line agency and is in talks with a number of creative shops.
Richemont also owns a range of other high-quality brands including Cartier and Jaeger.