French President Francois Hollande was expected to make a pitch for the Rafale, made by Dassault Aviation SA, when he and his team visit Malaysia next week, the source said.
"The ministry's top leadership have been promoting the Rafale," said the source, who was not authorised to speak to media on the negotiations.
"It's been done in promotional material for LIMA, and even at top government meetings," the source said, referring to this week's biennial Langkawi International Maritime and Aerospace Exhibition.
Malaysia was looking to buy up to 18 jets in a deal potentially worth more than $2 billion, the source said.
Defence Minister Hishammuddin Hussein was reported in media as saying that the race for new fighter jets has narrowed down to the Rafale and the Eurofighter Typhoon, built by BAE Systems.
The plan is to replace the Royal Malaysian Air Force's (RMAF) squadron of Russian MiG-29 combat planes, nearly half of which are grounded.
Dassault, which declined comment when approached, has kept a low profile in the race. BAE has been on a consistent and public campaign over the past six years to win the Malaysia contract, even establishing a regional office in the capital, Kuala Lumpur.
Steve Osborne, BAE's sales director for military air and information for the Asia Pacific region, said the Typhoon had a good chance of landing the deal as the company already supplied defence equipment to Malaysia.
"We believe this gives the government of Malaysia the confidence in us that they may go with us...," said Osborne.
An industry and a government source with knowledge of the negotiations said any decision would take at least two more years, as Prime Minister Najib Razak is focused on more domestic concerns in the run up to national polls that must be held by 2018.
Malaysia cut its total defence budget by 12.7 percent to 15.1 billion ringgit ($3.41 billion) this year, as Najib grapples with growing public discontent over rising living costs.
Besides Dassault and BAE, other suitors courting Malaysia are Russia's Sukhoi and Sweden's SAAB, which is selling its single engine Gripen.
Two industry sources said Sukhoi was also in talks with Indonesia, potentially to deliver up to two full squadrons of the new SU-35 planes. An Indonesian ministry official said in November that the ministry was looking to buy "nine or 10" of the planes, though the award had not been finalised.
SAAB, which is proposing a lease arrangement with Malaysia for use of the Gripen, is also in the running for a deal to deliver 36 single engine multi-role combat aircraft to the Philippines, according to an industry source who has direct knowledge of the negotiations.
"We're expecting a decision by the Philippine government between 2018 and 2020. Their procurement process is scheduled to happen between 2021 and 2024," the source said.
Defence spending in the Asia Pacific region is expected to hit $250 billion from 2016-20, IHS Janes Defence Weekly said in December, spurred by rising tension in the South China Sea where China has created several islands, worrying the United States and some of China's neighbours.
China claims most of the South China Sea, through which $5 trillion in ship-borne trade passes every year. The Philippines, Vietnam, Malaysia, Taiwan and Brunei also have claims.
($1 = 4.4230 ringgit) - Reuters
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