"GM had been in discussions with Spyker Cars about its interest in acquiring Saab," the Detroit firm's statement said.
"Despite the best efforts of all involved, it has become very clear that the due diligence required to complete this complex transaction could not be executed in a reasonable time," GM Europe president Nick Reilly said.
"In order to maintain operations, Saab needed a quick resolution. We regret that we were not able to complete this transaction with Spyker Cars. We will work closely with the Saab organization to wind down the business in an orderly and responsible manner. This is not a bankruptcy or forced liquidation process."
Earlier this week, GM agreed to sell some Saab assets to China's Beijing Automotive Industry Holding Co. State-owned BAIC will acquire the technology for Saab's 9-3 and 9-5 car models, turbine engines and gearboxes, allowing the Chinese firm to develop its own-brand cars using the Swedish carmaker's technology.
GM said that in the wind-down of Saab, it would satisfy debts including supplier payments and would continue to honor warranties and provide parts to Saab owners around the world.
Saab employs some 3,400 people in Sweden and sold just over 93,000 cars worldwide in 2008.
Industry is heavily centred around Trollhättan, on the west coast of Sweden.
"Trollhättan had a high level of unemployment before the financial crisis and at the moment it is at 11%. The shut down of Saab will seriously affect local society," said Eva Lindh-Pernheim, head of the Employment office in Trollhättan.
But politicians and authorities in the area are in agreement that they will not let the local area go down with Saab.
"Now is the time to be forward-thinking and open for new creative ideas. the most dangerous thing to do is to admit defeat and sink into depression. We must look on this as a chance to do other things," said Tore Helmersson, CEO for the development centre Innovatum Technology Park in the local area.