Buying any airplanes from Airbus would mark a major reversal for Seattle, Washington-based Boeing, which in 1996 signed an exclusive agreement to furnish American Airlines with all its planes, according to The Wall Street Journal.
American Airlines currently does not fly any Airbus aircraft.
The Financial Times, citing sources close to the deal, said the company plans to buy 250 narrow-body Airbus A320's and A320neos, which are expected to have improved engines, as well as 150 Boeing 737's.
There is also an option to buy 220 more airplanes, the Financial Times reports.
The Wall Street Journal says that the airline and Airbus reached a tentative deal last month to buy 200 A320s, with Airbus offering financing inducements as well as a more efficient jet engine.
The A320neo is expected to use 15 percent less fuel, a key factor for the airlines and one which allowed Airbus, a subsidiary of EADS, to sweep last months' Paris Air Show with virtually no competition.
But according to the Journal, Boeing countered with an improved version of its classic 737 airliner.
The Journal said the final decision could be modified at the last minute, and that the company's board of directors will meet Tuesday evening and Wednesday before announcing their decision.
The new version of the 737 is expected to enter service in 2017, two years after the A320 Neo.
Airbus came very close to winning the entire huge order, The Seattle Times reported online late Tuesday.
"Before anyone at Boeing knew about it, last month the airline signed an initial memorandum of understanding to buy A320neos, which will come with new fuel-efficient engines," the Seattle Times report said citing three unnamed sources familiar with the negotiation process.
"To head off that loss, within the last 10 days Boeing gave American a new proposal that offers the 737 jet equipped with similar engines," the report said citing the same sources.
"Boeing sales teams worked furiously over the past weekend to salvage the deal," the report added.
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