The source confirmed a report by German news weekly Der Spiegel, saying: "I expect a withdrawal by Forster within a week."
GM executive vice president David Reilly would replace Forster, as GM seeks to soothe anger over this week's decision to abandon a sale of Opel to Canadian group Magna and Russian partner Sberbank, the magazine said.
"I cannot comment," a spokesman for General Motors Europe and Opel told AFP, adding: "If there are any personnel decisions we will make a statement on it."
Forster was a keen supporter of Magna's bid.
On Thursday, GM chief executive Frederick "Fritz" Hendersen told reporters in Detroit that he would pick a new management team for Opel and its British sister brand Vauxhall within "days or weeks."
GM has decided to restructure Opel/Vauxhall itself, with the elimination of at least 10,000 jobs and possibly the closure of German factories, a move that has sparked widespread anger in Germany.
Germany is home to about 25,000 Opel workers, roughly half of GM Europe's total workforce, and the government had lobbied tirelessly for Magna's bid in hopes of keeping all the German plants running.
Berlin had promised €4.5 billion in state aid to Magna, angering other European countries where the loss-making Opel also has workers because of fears they would bear the brunt of badly needed restructuring.
GM is now expected to seek aid from Germany and other European countries to carry out a €3-billion revamp. A German government spokesman said Friday he expected GM to provide details of its plans next week.
German Economy Minister Rainer Brüderle has called GM's behaviour "totally unacceptable" while North Rhine-Westphalia state premier Jürgen Rüttgers said the move revealed "the ugly face of turbo-capitalism."
Hendersen acknowledged that "we have some fence-mending and repair that needs to be done."
Der Spiegel said that Reilly, who is British, brought with him Asian experience with GM's Chevrolet brand, which has increased sales in Europe as Opel has lost market share, calling the mooted nomination "a new provocation for Opel."
Reilly is considered a specialist in restructuring, and could make life difficult for workers at European plants, the magazine added.
Reilly, who has been based in Shanghai, also has experience at British Vauxhall plants in Luton and Ellesmere Port, two sites that welcomed the GM decision cautiously in hopes they might fare better than under Magna's ownership.
Just before GM made its announcement on Tuesday, Forster still appeared to believe the deal with Magna would go through, while saying it might take longer than expected.