The incident happened at around 1.50pm on Saturday 12 January 2019 at Aldi on Wallisdown Road.
It is reported that a man and a woman entered the store, put a number of items into their baskets and left the store without attempting to pay.
Staff from the store managed to stop the pair before they boarded a bus and recover all the items.
Police Sergeant Carmel Ryan, of Dorset Police, said: “We are continuing to investigate the incident and am appealing for anyone who recognises the man or woman, or has any information that could assist the investigation, to contact Dorset Police.”
Alternatively, contact Crimestoppers anonymously on 0800 555 111 or via www.crimestoppers-uk.org