Mr Demarco, who last year received the Edinburgh Award and the title of European Citizen of the Year, hailed the “magnificent” industrial building and said East Lothian would make the perfect setting for a huge new arts centre.
Campaigners are currently fighting plans to turn the power station into a massive marine energy park.
The 84-year-old said: “It’s the usual battleground between people with imagination and those that can only think of the obvious idea – of energy from the power station and God knows what else.
“If you are thinking of power stations, think of the fantastic history of the Tate Modern. We are waiting for a Tate of the north – and Cockenzie is the perfect setting. Everyone who believes in the future of Scotland should be backing this.”
The artist, who was a co-founder of the Traverse Theatre and has work in more than 2500 art collections around the world, said the “Tate North” would attract millions of visitors to East Lothian. The great hall of the power station building would act as the gallery’s main space, with outlying buildings also put to use.
And Mr Demarco said the new arts centre could even be used as a Festival venue.
The disused plant is currently owned by Scottish Power, which has planning permission to build a new gas-fired power station on the land.
But controversial proposals could also see parts of the power station and surrounding area – including the site of the Battle of Prestonpans – developed into a marine energy plant.
Mr Demarco slammed the plans as “completely bonkers”.
He said: “It’s madness. It is a typical lack of imagination.”
His plans have received strong support from local campaigners. Andrew Crummy, chairman of the 3 Harbours Arts Festival, said securing the power station as a new gallery venue could be the next step for the booming festival, which has been running for the last ten years and draws thousands of visitors to East Lothian.
“The Tate of the north is a great idea. To make it happen is a big step, but it’s still a great idea. The power station has that iconic element to it – a lot of people recognise it,” he said.
East Lothian Council declined to comment on the proposal, but Councillor Steve Brown, a member of the planning committee, said the plans would “have to be looked at” if submitted.
A spokesman for Scottish Power said it was continuing with demolition work at Cockenzie. He added: “The Scottish Government’s National Planning Framework identified Cockenzie as an important location for an energy hub.”