The firm is looking to restructure the bakery, which makes crumpets and pancakes, by the end of October, following a strategic review of UK operations. Back in March, workers feared for their jobs after Tesco reduced its business with the firm.
Allied has started a consultation with its 144 employees, which it said could result in about 40 redundancies.
The Bakers Food and Allied Workers Union is in talks with Allied although regional officer Roy Streeter said it was not particularly hopeful that it could reduce the number of job losses.
Tim Bright, site manager for the Liverpool bakery, said that while Allied's snacks business was growing, projected volumes were not sufficient to prevent it from having to restructure the operation.