In a statement, Genii Capital announced its "interest in making an offer for the acquisition of a majority stake in Saab SAS in a partnership with Ecclestone".
Genii said it would "aggressively work towards a successful closing of the transaction with all the relevant stakeholders of the company".
It added that Saab had "tremendous brand value in a number of key automotive markets, as well as an innovative image".
The privately-held firm already has links with Ecclestone after it last month bought a stake in the Renault Formula One team, allowing the outfit to remain in the sport.
Spyker, which confirmed late on Thursday it had made an improved bid, is hoping to gain Saab's technical resources and its distribution network, while bringing its entrepreneurial skills to the new group.
Swedish media reports on Friday named Jan Nygren, a former executive of the aerospace arm of Saab and former senior official in the defence ministry, as the head of a group of Swedish investors who had also submitted a last-minute bid for Saab.
Nygren confirmed to the Reuters news agency that he was part of a group of investors interested in Saab, but declined to offer more details about the deal.
"I can confirm that I am part of the group that has showed formal interest for saving Saab from winding down, but that's about it," he said.
Saab is one of four brands that GM is shedding as part of a massive restructuring effort that began in 2005 and accelerated last year when the US car maker went bankrupt.
Analysts have warned that about 8,000 direct and related jobs could be lost with Saab's closure.