The order would be worth $1.8 billion at list prices, although discounts are common. The Argentinian airline already has 26 similar planes.
The agreement was announced on Monday. A firm order has not yet been signed.
Boeing is getting ready to pivot from the current version of the 737, like the ones it is selling to Aerolineas Argentinas, to a new version called the 737 Max, which will have a new engine and other tweaks.
Boeing shares rose $1.11 to $122.53 in morning trading. Boeing shares are up more than 57 percent so far this year.
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