The discovery was made recently during the construction of the petrol station in the car park of the Littlehampton Road superstore, an ASDA spokesman confirmed.
Arun District Council said the Health and Safety Executive had been notified and the asbestos was now in the process of being removed.
Asbestos is a term for a group of minerals made of microscopic fibres. If you breathe in these fibres, they can damage your lungs and can lead to cancer in later life, according to the British Lung Foundation. Asbestos poses a risk to people when it is damaged or disturbed, by construction for example, as tiny fibres can be released into the air and breathed into your lungs.
An ASDA spokesman said the asbestos did not pose a risk to customers or people living nearby as it had been contained and would be removed safely.
He said: "We have been speaking to the council and contractors doing the work to make sure the right plans are in place to remove it."
It is the latest delay in the construction of the petrol station. On Tuesday, October 9, ASDA was told to halt construction by Arun as the correct permissions had not yet been granted.
He said the discovery should not affect the scheduled opening date of the petrol station, which is at the beginning of next year.