A deal between the two carmakers would create a combined market value of nearly $ 50 billion (£ 39.9 billion).
This is Fiat Chrysler's second attempt at a merger this year after it drew an agreement with Renault in June
Fiat Chrysler shares jumped 7.5% on Wall Street.
A potential merger will face significant political and financial obstacles.
Discussions remain in the early stages and there is no guarantee of a final deal.
However, if the two companies combine, PSA CEO Carlos Tavares is expected to lead the expanded group.
John Elcan, chairman of Fiat Chrysler and head of the Italian industrial dynasty Aneli, which controls the business, will retain the same position in the new company.
The merger of the two groups will result in a number of brands under one roof, including Alfa Romeo, Citroen, Jeep, Opel, Peugeot and Vauxhall.
- Fiat Chrysler withdraws bid for Renault
Negotiations come months after a proposed link between Fiat Chrysler and French carmaker Renault collapsed.
Fiat Chrysler described its bid for Renault as a "transformative" proposal that would create a global automotive leader.
The industry is moving towards electric models, along with stricter emission standards and the development of new technologies for autonomous vehicles. are putting increasing pressure on car manufacturers to consolidate.