A deal is expected to be reached within the next few months, according to the report.
Under the deal, the company would supply up to 30 Hawk aircraft for in-flight training.
Saudi Arabia recently ordered 72 Eurofighter Typhoon jets and pilots would train on the Hawk jets ahead of flying the Eurofighter.
BAE recently opened a new facility in Samlesbury, Lanchashire to manufacture the rear fuselage and tail for Lockheed Martin Corp.’s (NYSE: LMT) F-35 aircraft.
Japan could purchase $10 billion worth of F-35 jets under a foreign military sale, currently being explored by the U.S. Defense Security Cooperation Agency.
That purchase would include four conventional take-off and landing jets and an option to add 38 jets.