A spokesman for GM declined to comment.
Carlos Tavares, Renault's former COO turned Groupe PSA's CEO, has previously explained that purchasing Opel would give the French group the chance to become a "European auto champion", which could quickly exceed five million annual vehicle sales.
General Motors and Europe's PSA Groupe, which has Peugeot, Citroen and other vehicle brands, are edging closer to a deal that could potentially vault the French company into second place among automakers in Europe.
GM has been struggling to make money in Europe for years and almost sold a majority stake the unit in 2009.
PSA makes Peugeot and Citroen cars in Europe.
It wasn't a smooth negotiation process as there were some bumps in the road regarding the roughly $10 billion in Opel pension liabilities and also about whether a PSA-owned Opel would be allowed to go up against Chevrolet in China and other markets.
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Another issue in the talks has been how GM and PSA will manage the pension plan for Opel retirees, people familiar with the discussions have said.
That was the 16th consecutive loss-making year for GM in Europe, bringing its cumulated losses on the continent since 2000 to more than $15bn.
After fending off 2015 merger overtures by Fiat Chrysler with support from her board, GM Chief Executive Mary Barra agreed to target a 20 percent minimum return on invested capital and pay out more cash to shareholders.
The deal "will be sealed on Monday morning in France and in Germany", the source said, adding that both sides "were very enthusiastic and satisfied".
Reuters quoted sources as saying that PSA expected to make savings of up to 2 billion euros (£1.7bn) as a result of the takeover of Opel. There was also the matter of potential job losses, but PSA has made the promise to "respect the existing agreements".
Nevertheless, in a statement last week, PSA boss Carlos Tavares said he believes the tie up will offer "opportunity to create a European vehicle champion" with annual sales of over 5 million units.