Ryanair is in advanced talks to buy 100 of a high-density version of Boeing's 737 MAX jetliner.
The potential $10 billion deal could be finalised within weeks, according to a Reuters report.
The move comes two months after Boeing said it was studying plans to offer more seating in its upcoming 737 MAX by introducing a modified version with 200 seats, 11 more than the current maximum.
A deal for about 100 of those aircraft could be reached as early as the middle of September, a person close to the matter said.
"Ryanair does not comment upon, or engage in, rumour or speculation," a spokesman for the airline said.
A European spokesman for Boeing Co also declined to comment.
A new order from Europe's biggest budget carrier would mark a new phase in efforts by Boeing and European rival Airbus to appeal to ultra-low cost carriers.
Both manufacturers are adding seats to drive down the operating costs per seat, the key driver of aircraft economics.
Keeping up demand for the most popular types of airliner has in turn become the Holy Grail for both planemakers as they embark on ambitious production plans, with higher output volumes playing an important role in cutting costs and boosting margins.
In June, Airbus said it would increase the maximum number o fseats on its revamped A320 to 189, matching the capacity limit on the main variant of the Boeing 737 MAX and providing fuel savings of 3.5% per seat.
Weeks later, Boeing leapfrogged its European rival by announcing plans to offer a 200-seat version of the 737-8 MAX, which Boeing Commercial Airplanes chief executive Ray Conner said would offer unspecified cost savings of 5% per seat.
One industry source said Ryanair was expected to place a large order for the modified version of the 737-8 MAX and that this could happen "soon".
Another said Ryanair had been shopping for at least 100 and possibly as many as 150 of the higher-capacity aircraft.
Ryanair's chief executive Michael O'Leary would be able to take advantage of low interest rates and Boeing's keeness to have a large launch customer for its latest variant of the MAX.
He has long lobbied aircraft makers to produce a plane with just under 200 seats from the 189 on Ryanair's current 737 fleet to maximize the ratio of passengers to cabin crew. Airlines mus tprovide one flight attendant for every 50 passengers.
He offered at one point to buy planes from Chinese manufacturer Comac if they filled this requirement.
Ryanair last year signed a $15.6 billion contract to buy 175 Boeing 737-800 jets, the largest single order ever placed by a European airline with Boeing, with the first of the aircraft due for delivery later this month. It later upped the order to 180.
In July, O'Leary welcomed the decision to study a higher-density version of the 737 MAX and said he would maintain the order for current-generation 737.
Ryanair plans to boost its traffic to 120 million passengers a year by 2022 from just over 80 million today.