The order for the new 737 MAX 10 model may, however, include some aircraft originally ordered in a smaller size and upgraded to the proposed new 190-230-seat model, two of them said.
Lion Air will be a launch customer for the 737 MAX 10, Lion Air Group President Director Edward Sirait confirmed to Reuters. He did not immediately provide the number of planes it has ordered.
Boeing declined to comment.
Indian budget carrier SpiceJet Ltd also is among carriers seen as potential targets for the aircraft, a version designed to seat up to 230 people and blunt strong sales of the Airbus A321neo, two of the sources said.
SpiceJet could not immediately be reached for comment.
United Airlines also has been closely studying the aircraft as Boeing pitches for a marquee customer to launch the fifth variant of its 737 MAX family, two other sources said.
United Airlines Chief Executive Officer Oscar Munoz, contacted at an airlines meeting in Mexico, declined to comment.
Jet Airways Ltd, India's biggest full service carrier by market share, is in talks to buy 75 single-aisle aircraft from either Airbus or Boeing, people familiar with the matter said earlier.
If the deal is awarded to Jet's current supplier Boeing, it could include some of the new 737 MAX 10 model.
None of the sources agreed to be named because the talks remain confidential.
Private Indonesian carrier Lion Air ordered 201 Boeing 737 MAX aircraft in 2012 and placed options for another 150.
Such orders typically include the right to convert between different variants of each model.
Other airlines are looking at the Boeing 737 MAX 10, but some are nervous about committing to a new variant given patchy sales of some current models of the 737 MAX, whose success rests mainly on sales of the Boeing 737 MAX 8, the sources said.
At least one Chinese leasing company is said to be in negotiations with both manufacturers as Airbus tries to disrupt the launch, which sources say is planned for the June 19-25 air show. Airbus declined to comment on any ongoing negotiations.
Airbus sales chief John Leahy earlier criticised the 737 MAX 10 as a "marginal" airplane, implying sales would be poor.
Boeing marketing vice president Randy Tinseth told Reuters some airlines want more seats than existing versions and that the MAX 10 would be 5 percent more efficient than the Airbus A321neo. Airbus says its own plane is more efficient.
"It (the 737 MAX 10) is not a me-too airplane. We are focusing on a better airplane," Tinseth said on the sidelines of the International Air Travel Association annual meeting in Cancun, Mexico.
(Tim Hepher, Cindy Silviana and Aditi Shah - Yahoo Business News / Reuters)