The Clydebank winger was filming at Clyde's Broadwood Stadium in Cumbernauld with Celtic's Charlie Nicholas and the Scotland Under-21 coach, Tommy Craig, when he collapsed.
John Brownlie, the Clyde assistant manager, said: "Davie was fine one minute, then keeled over the next. It would appear to be very serious indeed."
First aid staff were on hand and Cooper was taken initially to Monklands General Hospital before being transferred to Southern General Hospital in Glasgow.
Richard Morgan, spokesman for the Southern General Hospital, said: "Davie Cooper's condition is critical. He is in intensive care in our Institute of Neuro-Scientists.
"He is being ventilated and we are trying to stabilise his position, which will be reviewed tomorrow morning. He suffered a brain haemorrhage."
Cooper, who was 39 last month, was set to retire from football as a player at the end of this season. He began his illustrious career with the Kilbowie club before moving to Rangers for £100,000 in 1977.
He won a host of honours in 12 years at Ibrox and was given a testimonial before joining Motherwell, where he won a Scottish Cup winners' medal in 1991. He rejoined Clydebank in December 1993.
Cooper won 22 Scotland caps and played in the 1986 World Cup finals in Mexico.Reuse content