Shares of Fiat Chrysler (FCAU) - Get Report jumped Tuesday after a report that the Italian-U.S. automaker is in merger talks with French automaker PSA Group (PUGOY) , which owns Peugeot and Citroen. 

PSA Group stock rose sharply, too.

A combination of the companies could create a colossus worth $54 billion, the current combined market capitalization of the two companies.

People familiar with the matter told the Wall Street Journal about the talks. One possible iteration for the deal would be an all-share merger of equals, one source told the paper. 

In this case, Peugeot Chief Executive Carlos Tavares would become CEO of the combined company, the source said. John Elkann, FCA chairman and head of the Agnelli family, which controls Fiat-Chrysler, would chair the merged entity. 

The sources said plenty of other deal structures are possible, and it's no sure thing that a deal will be completed.

The talks come after Fiat Chrysler pulled back in June from a plan to merge with Renault. The French government, a big Renault shareholder, and Nissan Motor (NSANY) , which has an alliance with Renault, declined to support the deal. 

Fiat left open the possibility of renewing talks with Renault. It also had been approached by Peugeot about a merger early this year, The Journal reported in March. 

Fiat Chrysler shares at last check traded at $14.19, up 7.2%, and PSA traded at $29.40, up 6%. Nissan shares were up 2.1% at $12.79.

The author owns no shares of any company mentioned.