The two-year-old service is looking for an agency to promote the Unwrapped Summer and Christmas catalogues.
PR manager Katie Abbots said four undisclosed agencies had made it onto a shortlist.
She added that the appointed agency will be given a year-long brief to promote Unwrapped in consumer press, and will also plan for a Christmas campaign.
The catalogues also contain corporate gifts and a wedding service. The latter uses the strapline ‘Forget the kettle, ask for some goats instead’.
Last year, Oxfam used Lloyd Northover for PR.