The preliminary selection, first reported by CNN, follows a fierce competition and is subject to approval at a board meeting later on Wednesday, which could still alter or delay the decision, the people said.
Such a deal would be worth $12.7 billion at list prices, but would typically involve steep discounts.
Delta and both planemakers declined comment.
The A321neo has a significant lead in market share over equivalent Boeing narrowbody models, but faces potential competition from a new mid-market jet being studied by Boeing and for which the US firm may start seeking offers next year.
But the endorsement from the second largest US airline by passenger traffic, known as one of the industry's pickiest buyers, brings respite to Airbus after a year marked by a slowdown in sales and internal management tensions.
It is also a boost for United Technologies subsidiary Pratt & Whitney, which is likely to win an engine contract to power the A321neo aircraft, industry sources said.
Airbus has been in discussions with Pratt & Whitney to ensure that enough engines are available to support the pledge to supply 100 jets to Delta as the US engine maker works through recent industrial problems, they added.
Pratt & Whitney, which competes with French-American venture CFM International to power the A320 family, declined to comment.