Earlier this year FCA Chairman John Elkann - a member of Italy's Agnelli dynasty that controls the company - stressed the family's commitment to the automotive industry. But he also added that they were prepared to take "bold and creative decisions" to help build a solid and attractive future for the company.
A source said an announcement from Italo-American FCA could provide some concrete although initial details but added the situation was still "fluid".
A separate source with direct knowledge of the situation confirmed that the Renault board will meet on Monday morning at 0800 local time (0600 GMT) to discuss the issue.
The meeting was first reported by French newspaper Le Figaro.
FCA has a highly profitable North American RAM trucks business and Jeep brand but has been losing money in Europe, where it may also struggle to keep pace with looming carbon dioxide emissions curbs.
Renault, by contrast, is an electric-car pioneer with relatively fuel-efficient engine technologies and a strong presence in emerging markets, but no U.S. business.
Any tie-up would likely face political and workforce hurdles, particularly in Italy. However, most of FCA's European plants are running below 50 percent capacity.
A tie-up between FCA and Renault would not preclude a consolidation of Renault's alliance with Japanese carmaker Nissan, a source told Reuters on Saturday.
The Renault-Nissan partnership, underpinned by cross shareholdings, has been strained by the scandal surrounding former chairman Carlos Ghosn, who was ousted after his arrest last year.
Speculation about the future of Fiat Chrysler, often seen as a potential M&A target, intensified after the death of long-serving former CEO Sergio Marchionne last year.
According to reports earlier this year the manufacturer had also restarted talks with France's PSA Group- which have been a recurrent theme over the years.
Fiat Chrysler and Renault together would have a combined market capitalisation approaching 33 billion euros ($37 billion) and total global sales of 8.7 million vehicles.
A tie-up that included Nissan would vault the ensemble to the rank of global No.1 carmaker with 13.8 million annual sales. It would also maintain a foothold in China, where both FCA and Renault are marginal players.
(Reporting by Laurence Frost, Gilles Guillaume and Inti Landauro in Paris, Pamela Barbaglia in London and Giulio Piovaccari in Milan Editing by Keith Weir) ((firstname.lastname@example.org; +39 02 6612 9743; Reuters Messaging: email@example.com))