"Discussions are at a very advanced stage," one source told Reuters.
The chief executive of Dassault Aviation said the firm was close to signing the first export contact for its Rafale fighter jets, according to an interview published in Le Figaro on Saturday.
Two industry sources told Reuters Egypt was discussing the purchase of 24 Rafale jets and a Fremm frigate from the French defence company, following a report in daily Les Echos, estimating the deal at 5 to 6 billion euros ($6.7 billion).
"The discussions are at a very advanced stage," said one of the sources.
CEO Eric Trappier declined to specify the country involved, but told Le Figaro there were "still several steps to cross" regarding a sale to Egypt.
"We have several prospects in the Middle East that are very active," he added.
Qatar is in talks with the company over firm orders for 24 of the jets and options for 12 more.
Dassault has also been trying to sell the Rafale to India since New Delhi chose the company over other foreign plane manufacturers in 2012.
But disagreements over cost and work-sharing have slowed talks over the sale of 126 of the fighters, while India's weakening economy has stretched government finances.
In December, the Indian defence ministry said the defence ministers of both France and India had agreed to finalise the sale in the deal worth an estimated $15 billion.
"We are conducting in-depth work with India in a very complex dossier in terms of industrial assembly," Trappier added. "And we have Rafale campaigns even further on, including in Europe."