The packaging giant, which bought Multigraphics only five years ago in a move into the point-of-sale (POS) market, confirmed that it entered into consultation with staff at the Bradford site on 20 June.
The 4,200sqm facility employs 60 people and specialises in retail display work such as POS, retail-ready packaging, floor graphics, outdoor media and banners.
DS Smith Packaging said in a statement: "If agreed during the consultation process, the proposal will involve the consolidation of all display manufacturing into our Ely site, while maintaining a sales and administration team in Bradford. This may result in redundancies at the Bradford site."
The business moved to assure customers that "usual service and quality will be maintained".
Last month FTSE 250-listed DS Smith group posted a 51% profit increase to £165m on revenues of £3.7bn, up 86% year-on-year. The figures are the first annual results since it completed the £1.3bn acquisition of Swedish-owned SCA Packaging in July last year.
Revenue from its UK operations, however, remained flat at £961m (2011: £960m).
Commenting on DS Smith's UK performance over the last 12 months chief executive Miles Roberts said: "While our core UK corrugated packaging business has delivered a robust performance, revenues for the overall UK division have been impacted by continuing weakness in the paper market, as a result of which, prices and demand have remained subdued.
"Focus going forward would be to continue growing the packaging and recycling businesses, while reducing our exposure to paper manufacturing and disposing of non-core businesses and assets."
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