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.
Fiat Chrysler said the merger would create the world's third largest automaker, with annual sales of 8.7 million vehicles.
The proposed deal would merge the two carmakers under a listed Dutch holding company. After a 2.5 billion euro dividend paid to existing FCA shareholders, investors in each company would receive half of the new entity.
Industry shifts toward electric models, along with stricter emissions standards and the development of new technologies for autonomous vehicles, have put increasing pressure on carmakers to consolidate.
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 a year ago.
A report over the weekend surfaced indicating that FCA and Renault have been in talks for a tie-up of their operations "that could include joining large portions of their businesses".
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Any tie-up would likely face political and workforce hurdles, particularly in Italy.
Renault and Fiat Chrysler estimate cost savings of more than €5 million (¥613 million) as a result of their deal, and an additional €1 million in savings for alliance partners Nissan and Mitsubishi Motors.
Such a merger would show "our capacity to respond to European and French sovereignty challenges in a globalised context", she said.
Early this year, rumours circulated that Renault was interested in Fiat-Chrysler after its hopes for a full merger with Nissan or even French competitor PSA were dashed.
The French government has a 15% stake in Renault and the carmaker's chairman, Jean-Dominique Senard, presented an FCA-Renault merger plan to French finance minister Bruno Le Maire on Friday, Les Echos reported.
Anticipating such sensitivities, FCA stressed "new opportunities for employees of both companies" under the merger.
"The benefits of the proposed transaction are not predicated on plant closures, but would be achieved through more capital efficient investment in common global vehicle platforms, architectures, powertrains and technologies", FCA says.