Police have released a CCTV image of a man they want to speak to in connection with the incident.
The offender approached the couple on Thursday, April 21, while in the Morrisons store in Beacon Street and convinced them to drive him back to their home.
He then stole the purse, which contained bank cards and a small amount of cash, leaving the victims shaken but unhurt.
Police were called at 11.25pm to an address near Beacon Street.
At about 11.45am the same day, it is believed the suspect used the stolen card to purchase a mobile phone top-up in Lichfield.
The suspect is described as Asian, roughly in his early 40s, and approximately 6ft tall, with a balding head.
At the time of the offence, he was wearing a brown or dark-coloured jacket.
Officers would like to speak to anyone who may have witnessed the offender approach an elderly couple in the supermarket.
Anyone with information should contact them on 101, Facebook or Twitter, quoting incident 252 of April 21.
Alternatively, contact Crimestoppers anonymously on 0800 555 111.