Cops rushed to the scene when the grim discovery was made beneath the site at around 2.10pm on Leech Street, Stalybridge.
It is believed the findings were a “skull and shoulder blade” that belonged to a human being.
A photograph was posted on Facebook showing a contractor and council officials looking down into the supermarket car park in Greater Manchester.
The site is thought to be a former burial ground on the site of an old chapel, reports the Manchester Evening News.
The car park belonged to Tameside Council until it was sold to the supermarket giant.
Cops have now launched an investigation to confirm whether the bones found were from a human being.
Witnesses reported seeing police and council officials at the site on Tuesday afternoon.
They claim work stopped abruptly after heavy machinery churned up the old car park behind Melbourne Street.
It is understood police remained at the scene throughout the afternoon.
They say the remains are yet to be moved and a police tent covering the site remains in place.
A similar discovery of “human remains” was found when a canal in the town centre was dug out, exposing plots from an old Methodist cemetery.
