Opel has been a problem for G.M. for decades. Once a serious rival to Volkswagen, it began losing market share in the 1990s, which was also the last time it made a profit. While the Volkswagen Group has become the world’s biggest carmaker, Opel slipped to Europe’s margins.

“Opel has been hemorrhaging money for the last 16 years, so hard decisions are on the table in Mary Barra’s version of a profitable G.M.,” said Rebecca Lindland, an analyst with the auto-research firm Kelley Blue Book.

The G.M. unit suffered from frequent turnover in top management, friction with labor representatives and products that buyers perceived as dull or inferior. Among other things, Volkswagen was faster to offer cars with diesel motors, which are popular in Europe because of their superior fuel economy compared with gasoline vehicles.

Shares of G.M. closed up 4.8. percent on Tuesday.

In 2009, the company was on the verge of selling Opel to a consortium made of Magna, an auto parts supplier based in Canada, and the Russian lender Sberbank. But the American carmaker pulled out of the deal at the last minute, reportedly because of fear that the takeover would give the Russians access to its patents and technology.

Since then, Opel’s financial situation has improved under the leadership of Karl-Thomas Neumann, a former Volkswagen executive. News of the merger talks came as G.M. reported that its European division had posted a loss of $257 million in 2016, an improvement from a loss of $813 million the year before.

Volkswagen’s emissions scandal also presents a chance for competitors to challenge the German carmaker’s dominance. Volkswagen’s market share, including other company brands like Audi and Porsche, slipped in 2016 to 23.9 percent from 24.6 percent the year before.

But even combined, PSA and Opel would have a lot of catching up to do. Both lost market share in Europe last year to Renault and Fiat Chrysler. And all of the mid-price brands have lost buyers to BMW and Daimler, which makes Mercedes vehicles. Those two companies have increasingly offered products priced within reach of middle-class customers.