Sources previously told Reuters that rivals Delta Air Lines Inc
The airlines are chasing access to JAL to help expand in Asia via code-sharing agreements.
Haneda, Japan's main domestic airport, is the world's third-busiest by passenger numbers and is adding international flights. Tokyo's Narita international airport also plans to expand airline slots.
If JAL opts for investment from Delta or Air France-KLM, it would be defecting from the Oneworld Alliance, a move analysts say would deal a huge blow to a group that includes British Airways
Oneworld would lose JAL's more than 400 flight slots a week at Narita, twice those of Japan's No.2 carrier All Nippon Airways (ANA) <9202.T>, as well JAL's growing business in China.
ANA is in the Star Alliance, with Air China Ltd <601111.SS>, Singapore Airlines Ltd
Losing JAL would mean Oneworld suddenly has to rely more on American Airlines' few slots in and out of Narita, said Nomura analyst Makoto Murayama. AMR is likely to fight that at all costs.
American Airlines is the No.4 international carrier at Narita, with about 70 slots a week.
JAL's suitors are each discussing investing $200-$300 million for a minority stake and a code-sharing relationship, but talks are fluid and those numbers could change, said the source, who was not authorized to discuss the talks publicly.
Representatives for JAL declined to comment, saying only that nothing had been decided.
Analysts said JAL would have to weigh the advantage of teaming up with Delta, which became the world's biggest airline when it acquired Northwest Airlines last year, against the significant cost of leaving the Oneworld alliance.
If you just look at what the companies can offer, then Delta would make more sense as an ally because it has more services between Japan and North America, Credit Suisse analyst Osuke Itazaki said, noting a tie-up with Air France-KLM would not expand JAL's network by much.
Delta and Air France-KLM are members of the SkyTeam group, with Korean Air <003490.KS> and Russia's Aeroflot
JAL shares, which had dropped by more than a fifth this year before news of the talks with Delta and AMR, fell 3.4 percent on Tuesday in a flat market <.N225>, erasing nearly half their previous day's gains.
JAL, which is undergoing a state-supervised restructuring, prefers American Airlines because of the Oneworld alliance, the source said, but the Japanese government prefers Delta or Air France-KLM, which it sees as financially healthier than American.
JAL lost about $1 billion last quarter and is under growing pressure to raise money and slash costs after securing a 100 billion yen ($1.1 billion) government-backed credit line this year. The airline has forecast a net loss of 63 billion yen ($693 million) for the year to end-March.
As at end-March, JAL had total liabilities of 1.44 trillion yen ($15.8 billion), with the Development Bank of Japan its biggest long-term lender.
It plans to cut overseas flights and increase personnel cuts over the next three years to reduce operating costs by 30 percent, Japanese media said. It will scrap 20 international flights by March 2012, the Nikkei said, resulting in a 20 percent drop in sales from overseas flights.
The airline hopes to raise around 100 billion yen from foreign carriers, Kyodo news agency said, adding that Korean Air <003490.KS> was also in talks with JAL.
JAL plans to axe another 1,000 jobs, bringing total staff cuts to around 6,000, Kyodo said, adding JAL planned to cut 24 international routes, including flights connecting with China. ($1=90.90 Yen)
(Additional reporting by Nobuhiro Kubo and Mayumi Negishi) (Editing by Ian Geoghegan)