The comments come a week after Boeing received approval for its 737 MAX to fly again following a 20-month grounding after two fatal crashes.
"I think it is important for Boeing to announce some customer orders and we would certainly be very keen to be at the front of the queue because the MAX 200 is a great aircraft," O'Leary said, referring to the 197-seat variant of the plane.
O'Leary, whose airline currently has 135 firm orders for the MAX 200, declined to comment on how many additional planes may be ordered. Earlier this month he ruled out an order for the larger MAX 10 in the short term.
"I would be reasonably hopeful, but there is a lot of work for us to do with Boeing over the next couple of weeks and months if we're going to reach an agreement on the existing order pricing and increasing the scale of our current orders," O'Leary said, when asked about the chances of a deal.
"I would hope to reach agreement if not before the end of the year, very early in the new year."
The U.S. planemaker is trying to secure eye-catching deals with other major carriers to sell the 737 MAX at heavily discounted prices to help rebuild what was once its fastest-selling product, industry sources said.
But several of its largest customers are struggling in the wake of COVID-19 restrictions that have devastated the global airline industry.
Boeing's largest customer worldwide, U.S. based Southwest Airlines, said last week it would just take new MAX jets to replace jets it's retiring rather than grow its fleet, and raised the prospect of scaling back its fleet due to the pandemic.
A new Ryanair order would be part of a deal with Boeing on compensation for delays to MAX deliveries. O'Leary said he expected the first 25-30 MAX jets to be delivered in time to fly next summer.
(Reporting by Conor Humphries; additional repoting by Tim Hepher; editing by Jason Neely and Mark Potter)
By Conor Humphries