The man was found in the kitchen at The Shehadeh Medical Centre in Dell Road at 3pm on September 6.
He was challenged by a staff member and left. Some food from the fridge and a hand blender are believed to have been taken.
The man is described as white with dark brown curly hair. He was wearing a grey tracksuit.
Anyone with information is asked to contact Pc Aiden Walsh at Grays police station on 101 or Crimestoppers on 0800 555 111.