Proposals to invest in ailing Malaysia Airlines include one from Air France-KLM, which wants as much as 49%, while Japan Airlines is looking at a 25% stake, people with knowledge of the matter have said.
Domestic carrier AirAsia Group Bhd and Malindo Air, the Malaysian arm of Indonesia's Lion Air, have also submitted proposals, the people added.
Air France-KLM said that it had previously held talks with Malaysia Airlines' owners but was not currently involved in the sale process.
Malaysia's government has found the proposals from foreign airlines more attractive, but the sovereign wealth fund that owns Malaysia Airlines favours a deal with AirAsia, one of the sources said.
"The bids from the foreign carriers are more comprehensive and strategic as both plan to capitalise on the strategic location of Malaysia for their operations," said the source.
The Malaysian government has been seeking a strategic partner for its national airline, which has struggled to recover from two tragedies in 2014 - the mysterious disappearance of flight MH370 and the shooting down of flight MH17 over eastern Ukraine.
That year, it was taken private by sovereign wealth fund Khazanah Nasional Bhd, which paid 1.4 billion ringgit ($345 million) for the 30% of shares it did not already own.
The sources declined to be identified as the discussions are confidential. Representatives for AirAsia and Malindo did not immediately respond to requests for comment.
In an e-mailed statement, Air France-KLM said it maintained the "active yet pragmatic" approach to industry consolidation it had outlined to investors in November.
"Air France-KLM had previously been in contact with Malaysia Airlines' shareholders, but at this stage Air France-KLM is not a current party to the sales process of Malaysia Airlines," the Franco-Dutch airline group said.
Japan Airlines (JAL) said that it is looking to expand its partnership with Malaysia Airlines through their joint venture, but declined to comment on reports of a potential investment in the company.
The government has received five proposals as part of a review that started last year, Malaysian Prime Minister Mahathir Mohamad said this week, although he declined to name the suitors.
There is no official timeline for a deal, but one source has said the government wants to get an investor finalised this quarter.
Mahathir And Khazanah At Odds
Last year, Malaysia Airlines signed a joint venture agreement with JAL covering flights between Malaysia and Japan, which the Japanese airline said could be expanded in the future to cover US flights.
Malaysia Airlines and JAL are both members of the oneworld airline alliance, while Air France-KLM is part of the rival SkyTeam alliance.
Sources said that Air France-KLM had proposed setting up a hub for maintenance, repair and overhaul services in Malaysia, while Japan Airlines had offered to make the Southeast Asian country its regional hub, including for low-cost flights.
"An international solution is probably better in this situation as AirAsia would have competition concerns," one of the sources said.
"This is still a work in progress but the story is around the potential for a massive hub in Southeast Asia and it's clear that international airlines see value in Malaysia Airlines because of this," the source said.
Business news website Focus Malaysia said this week, citing an official document, that Khazanah had been pushing for AirAsia to merge with Malaysia Airlines.
It also said that AirAsia boss Tony Fernandes had proposed a three-way merger between the company, its long-haul unit AirAsia X and Malaysia Airlines.
Khazanah, which appointed Morgan Stanley last year to advise on potential options for the airline, said that it is working closely with the government.
"While there have been several proposals in this regard, a review of the options available to us is still ongoing," it said in a statement.
But Mahathir, who is also chairman of the board at Khazanah, said he was "not completely happy" with the way the fund had been evaluating the proposals.
"Unfortunately, Khazanah has got its own agenda so I have to check them," he said.