The victim, aged 46 from Wigan, was reportedly carrying out maintenance on the vehicle in the coach park at about 12:30 BST on Wednesday.
Police said he was pronounced dead at the scene and his next of kin have been informed.
Cheshire Constabulary said the bus is thought to have been stationary and unoccupied at the time.
A police investigation is under way and the Health and Safety Executive has been informed.
A man has died after becoming trapped under a double-decker bus parked outside Chester Zoo.