After failing for years to win an order for its warplane, France has sold 24 Rafales each to Egypt and Qatar in recent months and is in talks to finalise the sale of another 36 to India.
"There should be two other export contracts for the Rafale by the beginning of next year," not including India, the source said.
"The most advanced discussions are with Malaysia and the UAE," the source added.
In a further development, the source said that France was negotiating with India for options to supply further aircraft on top of the 36 Rafales the country has provisionally agreed to buy.
In April, Indian Prime Minister Narendra Modi said he had ordered 36 "ready-to-fly" Rafale fighters to modernise his country's warplane fleet, dealing directly with the French government after three years of inconclusive negotiations with the plane's manufacturer, Dassault.
India has signalled any further purchases will come though government channels, raising doubts over the future of the stalled commercial negotiations with Dassault for 126 jets
The recent spate of Rafale export orders has shaken up the global defence market and given fresh momentum to the French warplane as available production slots begin to dwindle.
Analysts and diplomats say the appetite for the jets has also risen as a result of the United States' diminishing influence in the Arab world along with wider security concerns.
However, Dassault still faces tough competition from U.S. and European rivals.
Kuwait is expected to announce soon an order for 28 Boeing F/A-18 E/F Super Hornets, a $3 billion-plus deal that will keep the jets' St. Louis production line running well into 2019, according to people familiar with the deal. .
Malaysia, which wants to replace its fleet of Russian MiG-29 fighters, is looking at the Rafale, the F/A-18, Swedish firm Saab's Gripen and the Eurofighter Typhoon.
While a Malaysian decision had been expected this year, aviation industry executives have warned that fiscal troubles due to lower oil and commodities prices could lead to delays in placing the order.
Indonesia, which needs to replace ageing U.S.-built F-5s, is reported to be studying the Rafale, Eurofighter and Russia's Sukhoi Su-35 as well as Sweden's Gripen and the Lockheed Martin F-16. The Eurofighter consortium comprises Airbus Group , representing Germany and Spain, Italy's Finmeccanica and Britain's BAE Systems.
By Cyril Altmeyer