"We have agreed to continue detailed talks with both Magna and RHJI to secure Opel's future," John Smith, GM's chief negotiator for the sale of Opel, said in a statement, citing "a good and thoughtful discussion" of the offers.
Of the two bids remaining, Canadian auto parts maker Magna enjoys the support of the German federal government, the governments of the regional states where Opel has factories and the powerful unions.
While the final decision lies with GM, the German government is involved as it is set to stump up billions of euros in loan guarantees to sweeten any takeover deal in a bid to save tens of thousands of jobs.
A spokesman for Chancellor Angela Merkel said on Wednesday that Berlin's preference for the Magna proposal - backed by Kremlin-controlled Russian bank Sberbank - was unchanged following an initial examination of the bids.
Berlin hopes to thrash out an agreement with GM in the next few weeks, the spokesman added, although a final decision on who wins Opel will probably not occur until much later.
The regional governments involved in the talks are also backing the Magna bid, with the state premier of Thuringia saying that all four states where Opel has plants favoured the Canadian proposal.
In an interview with the local Thüringer Allgemeine Zeitung on Thursday,
Dieter Althaus said: "The Opel states are united."
Magna is the only potential investor likely to provide a sustainable future for the company and maintain the plants in the state, Althaus said. And the influential IG Metall metalworkers union also dismissed the proposal from RHJ International, a Belgium-based holding company backed by US investment fund Ripplewood.
The union said RHJ was only interested in making a quick buck from Opel and was not serious about investing in the company to turn around its fortunes. "IG Metall is not prepared to participate in a concept for the short-term interests of the shareholders," said the union's head Berthold Huber.
Despite the broad support for Magna, the battle is far from won, as GM is thought to be leaning towards RHJ. Nevertheless, as Merkel's spokesman said on Wednesday, the deal can not go ahead without Berlin clearing the billions of euros of loans and guarantees for its preferred candidate.
On the face of it, there is not much to differentiate the two bids.
Magna and Sberbank are hoping to acquire 27.5 percent each of Opel, leaving GM itself with 35 percent and 10 percent of the company in the hands of the workers. According to the Russian press, Magna has also demanded GM's intellectual property rights to be included as part of any deal.
In late May, the German government agreed to support the Magna bid with cheap loans and loan guarantees and said the plan would entail the loss of around 2,600 jobs in Germany, with a further 8,500 elsewhere in Europe.
For its part, RHJ is seeking €700 million less in state guarantees than Magna and would buy a 50.1 percent stake for €275 million. RHJ International is thought to be planning around 8,100 job losses Europe-wide in the Opel business.
BAIC offered €660 million for a 51 percent stake and wanted considerably less - €2.6 billion - in German government guarantees. However, it was always seen as the least favoured bidder and now joins the failed bid of Italian car giant Fiat on the scrapheap.