Citing sources close to the negotiations, Reuters reports AirAsia Group and Lion Air budget arm Malindo Air have also submitted proposals.
The Malaysian government has been seeking a strategic partner for the country’s national carrier for some time.
The airline has been beset by tragedy in recent years after flight MH370 disappeared en route to Beijing in March 2014 before flight MH17 was shot down in eastern Ukraine just four months later.
Air France-KLM, Japan Airlines, AirAsia and Malindo did not respond to Reuters’ request for comment.
Malaysian prime minister Mahathir Mohamad said five proposals were received during a review, which started last year.
Malaysia Airlines currently shares a joint venture agreement with JAL, both of whom are oneworld alliance members. Air France-KLM is part of rival SkyTeam.
