The troubled jet has been grounded since March 2019, following a second fatal crash of the 737 Max.
Boeing is seeking to persuade safety officials that modifications of flight control software will prevent any repeat of the two accidents, which killed a total of 346 people.
The biggest European budget airline has 210 of a special variant of the Boeing 737 Max on order. The Max 200 design adds an extra eight seats, to take the capacity to 197 passengers.
Ryanair’s chief marketing officer, Kenny Jacobs, told a news conference in Madrid: “We now think we will get [the Max] in March or April this year, looks more like April than March, and we think we will get up to 10 Max aircraft.”
He made it clear that the decision to return the Boeing 737 Max to service is in the hands of the Federal Aviation Administration (FAA) and other regulators.
Ryanair has 210 of the planes on order, but none was in service at the time the worldwide ground stop took effect.
Mr Jacobs said: “We still think the Max is a great aircraft. Our focus, their focus now is just to get the Max flying.”
Ryanair currently operates only Boeing 737-800 aircraft.
Originally Ryanair expected to receive the first of the new planes in April 2019 and to start flying them the following month from Stansted.
According to Jim Liu of Routes Online, the first routes for the Boeing 737 Max planned from the Essex airport in May 2019 were set to be Tenerife South and Thessaloniki.
Initially each was to be served three times a week by the Max, with flights by 737-800s on other days. By July 2019, Tenerife was set to become the first destination that Ryanair served exclusively with the new plane.
Other “first wave” destinations from Stansted were Alicante, Athens, Bari, Brindisi, Dortmund, Madrid and Palermo.
The airline has stressed that no final decision has been made about allocating the aircraft – and that type allocations can be changed at any time up to departure.
Online polls conducted by The Independent indicate widespread concern about flying on the Max.
Some US airlines have said that passengers unhappy about flying on the jet when it returns to service will be able to switch to alternative flights.
In December 2019, the chief executive, Michael O’Leary, told The Independent: “During the first year, you’ll have a 10 per cent chance you’ll be on a Max aircraft.
“Will anyone know or care? Frankly, I don’t think they will.”
The Independent has asked Ryanair for a response following Mr Jacobs’ comments.
Before the grounding of the Boeing 737 Max, the two airlines using the plane widely from the UK were Norwegian and Tui Airways.
Both are expected to return the aircraft to service in 2020. But Ryanair aims to fly the jet in far greater numbers.
The Irish carrier is the safest airline in the world in terms of passengers flown without a fatal accident.