The deal could be in the form of an all-stock deal, the report said.
Fiat Chrysler shares rose sharply after the report and were up more than 7% in late afternoon trading.
Fiat Chrysler and Peugeot had no comment.
Investors have speculated for several years that Fiat Chrysler was hunting for a merger partner, encouraged by the rhetoric of the company’s late chief executive, Sergio Marchionne. In 2015, Marchionne outlined the case for consolidation of the auto industry, and tried unsuccessfully to interest General Motors in a deal.
Peugeot and Fiat Chrysler had discussed a combination earlier this year, before Fiat Chrysler proposed a $35 billion merger with French automaker Renault SA.
Fiat Chrysler Chairman John Elkann broke off talks with Renault in June after French government officials intervened, and pushed for Renault to first resolve tensions with its Japanese alliance partner, Nissan.
Following the collapse of the Renault merger plan, Fiat Chrysler CEO Mike Manley left the door open for talks with would-be partners, but said the Italian-American automaker could go it alone despite mounting costs to develop electric vehicles and comply with tougher emissions rules in Europe, the United States and China.
Peugeot CEO Carlos Tavares dismissed the idea of a combination with Fiat Chrysler during a discussion with reporters at the Frankfurt auto show last month.
“We don’t need it,” Tavares said when asked whether he was still interested in a deal with Fiat Chrysler.
Fiat Chrysler has a commercial vehicle partnership with Peugeot.