GM, which has now filed for bankruptcy protection in the United States, placed Saab on the market in February as part of its attempts to slim down its brand range and return to profitability.
A Sveriges Television (SVT) report on Thursday said Koenigsegg and a group of Norwegian investors had signed a letter of intent to buy Saab.
Bård Eker, whose holding company Eker Group holds a 49 percent stake in Koenigsegg, confirmed his interest in the Swedish automaker in an interview with Norwegian newspaper Dagbladet.
"We think it is possible and we have several good solutions to bring with us into Saab," Eker said.
Commentators in Sweden have questioned whether Koenigsegg, which produces just 18 high-end sports car a year and employs only 45 people, would have the financial muscle or industrial know-how to run Saab.
Founded in 1994 by Swedish businessman Christian von Koenigsegg, the company posted a turnover of 106 million kroner (10 million euros, 13 million dollars) in 2008.
Eker told Dagbladet that there were "several investors" backing the bid.
"But I don't want to comment on the amount of money and who is involved," he said. "I want to make one thing clear. We are not buying Saab just to chop it up. That's not what we do."
The Eker Group was unavailable for comment and Saab spokesman Joe Oliver refused to comment.
GM also kept silent.
"We're not making any comment at this time. We continue to work towards a resolution for the sale of Saab," said GM Europe spokesman Chris Preuss.
Saab sold 93,000 cars worldwide in 2008, according to its website.
It owes 9.7 billion kronor ($1.3 billion, 924 million euros) to GM - its largest individual creditor - as well as 347 million kronor to the Swedish government. Other creditors are owed 647 million kronor.
The automaker employs about 3,400 people in Sweden. Including suppliers, some 15,000 jobs in the country are believed to be at risk if the company were to disappear.