An announcement could be made later on Tuesday alongside the airline's quarterly financial results, the source said on condition of anonymity, adding that a separate Boeing deal was also expected.
The Airbus deal would be worth around $1.99 billion based on the European manufacturer's list prices.
An Airbus spokeswoman declined to comment.
Reuters earlier reported ANA was nearing a deal to purchase 30 Boeing Co 737 MAX jets worth $3.5 billion at list prices, according to two people familiar with the matter.
(Reporting by Tokyo bureau; Editing by Simon Cameron-Moore)