Police and paramedics were called to the car park at the Tesco store in Rousey Drive at about 3.10pm on Sunday – but the 73-year-old man was pronounced dead at the scene.
Officers are keen to speak to any shoppers who may have seen the man’s blue Nissan Micra driving into the parking lot at around 3pm.
In a statement, Sergeant Chris Smith said: “We are working to establish the exact circumstances at this time and although we believe that the man has taken ill at the wheel, we are asking any witnesses to come forward.
“I would urge anyone who saw the blue Nissan Micra being driven in the car park around 3pm on Sunday afternoon to contact us. We would also ask anyone with dash-cam footage to come forward.
“Anyone with information should contact 101 quoting reference number 2121 of Sunday January 24.”