The brand has not begun a pitch. J Walter Thompson is the incumbent on the account and has held the business since August 2012.
Ogilvy & Mather, a fellow WPP agency, had the account before JWT.
Tilda has been largely dormant in terms of advertising since appointing JWT but the company is said to be reviewing its marketing strategy in the wake of a change of ownership and management team.
Tilda was purchased in January 2014 for a reported £218 million by Nasdaq-listed Hain Celestian, which also owns the Linda McCartney product range. Before the deal, Tilda had been family-owned for 40 years.
Tilda and JWT declined to comment.
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