The statement did not say whether the talks were aimed at a full-blown merger or a looser alliance.
Italian-American firm Fiat Chrysler has long been looking for a partner to help shoulder investments in the capital-heavy industry, where it can cost billions to develop new models and where manufacturers are having to keep pace with new technologies such as electrification.
Talks this year with another French car maker, Renault, failed over French government concerns over the role of the Japanese partner Nissan.
Fiat Chrysler Automobiles was formed in 2014 out of a merger of Italian car maker Fiat and the American company Chrysler, which Fiat brought back from the brink of bankruptcy.
Any tie-up between the group and French rival PSA Peugeot would bring a number of brands under the one roof, including Alfa Romeo, Citroen, Jeep, Opel, Peugeot and Vauxhall.