The company has shortlisted Kitcatt Nohr Alexander Shaw, Clark McKay & Walpole and Souk.
The confectionery brand is looking to relaunch the service in the summer, following a poor performance by its high-street shops. It has previously handled the business in-house.
Thorntons revealed a 4.9 per cent drop in like-for-like sales in its shops over the Christmas period. This was despite running a high-profile television campaign created by Miles Calcraft Briginshaw Duffy.
MCBD is unaffected by the review.
