The move could affect tens of thousands of jobs across Europe including 25,000 at Opel plants in Germany, as well as boosting a giant reconfiguration of the global auto industry brought on by the world economic crisis.
A GM source confirmed that the US auto giant's board had met in Detroit on Tuesday but declined to provide details on their plans. Union sources in Europe said they expected the board to answer their plea for a speedy resolution.
According to a report in the Wall Street Journal quoting a source close to the matter on Wednesday, however, the GM board may end up postponing any move on Opel until later this month - a delay that would spark anger in Europe.
"It's conceivable that they will not make a decision," the source said.
In a bid to up the pressure on GM, the European unions at Opel and its British twin Vauxhall published an open letter on Tuesday imploring GM to make a speedy decision about what to do with its European brands.
A top adviser to German Chancellor Angela Merkel added to the calls on Wednesday, calling for a "quick decision" from GM.
"It is important for the employees and Opel plants in Germany that we are informed as soon as possible," the adviser, Michael Meister, told AFP.
The deal would include all of GM Europe's operations except for Swedish unit Saab, which has been sold separately to luxury carmaker Koenigsegg.
Berlin favors a sale to a consortium made up of Canadian auto parts maker Magna International and Russian state lender Sberbank, but GM is also considering an offer by the Belgian holding group RHJ.
The US auto giant could also keep the unit it has owned for 80 years.
German Finance Minister Peer Steinbrück discussed the matter with his US counterpart Timothy Geithner at a G20 meeting on Saturday, and indicated that he was expecting a decision by the board this week.
"I have told him what the (German) government's position is, that we are very much interested that the current vacuum will finally be filled," he said. "The government still favors the industrial policy concept of Magna and therefore this partner."
The US government, which holds a 60 percent stake in GM, has said it will not get involved in negotiations.
Steinbrueck acknowledged that "the decisions will clearly be made based on the very narrow economic interests of General Motors."
But he noted that Germany's willingness to provide up to €4.5 billion in aid to Opel "is clearly linked to this partner."
A source at Magna who declined to be named told AFP that the company had no intention of withdrawing its offer and was "hopeful there will be some kind of conclusion in the next week or two."
GM has been dragging its feet on deciding the fate of Opel since it emerged from bankruptcy protection after a massive government bailout on July 10.
The company had said it was interested in selling a majority stake in its European operations.
But recent press reports have speculated that the "new GM" would like to preserve the brands in order to maintain access to the European market and help it develop smaller, more fuel efficient vehicles.
The Wall Street Journal also said last week that GM expected to get €1 billion in public aid from Britain, Poland and Spain on top of state support already provided by Germany.
GM rival Chrysler, which emerged from bankruptcy a month earlier, also has a foot in Europe through its alliance with Italy's Fiat.
Keeping Opel within GM would be a blow for Chancellor Angela Merkel, who is in the midst of campaigning for the September 27 elections. She recently renewed her support for the Magna-Sberbank bid.
The head of General Motors in Europe said last week that Magna-Sberbank would "most likely" win the drawn-out battle to take over Opel but did not rule out that GM could keep control of its European operations.