Both French business website LaTribune and the Financial Times named the American company as the likely suitor, reporting that an agreement would see the two groups joining forces to build cars and components in Europe.
Any deal would likely fall short of a full merger with each company retaining its own brands.
On Tuesday Peugeot confirmed it was "looking at potential co-operations and alliances."
"Discussions are taking place and there can be no certainty at this stage that these discussions will result in any agreement," the company said in a statement.
Peugeot has been known to be in the market for a partner since 2009 when its chairman said the group would be open to an alliance.
Last week the company reported a loss of €497 million ($658 million) for the second half of 2011.
The PSA Peugeot Citroën group was created in 1976 when Peugeot acquired a majority stake in the then bankrupt Citroën. It is the world's eighth-largest car maker in terms of sales.
General Motors is the world's biggest car manufacturer and employs over 200,000 people.
Peugeot Citroën shares surged 9 percent on the news as the French stock market opened on Wednesday morning.