The talks are part of a series of negotiations between Boeing and several airlines over jet orders or compensation after the 737 MAX was banned worldwide following two fatal crashes.
Boeing and Alaska Airlines, which is part of Alaska Air Group Inc, declined to comment.
Any deal would be subject to U.S. Federal Aviation Administration approval of proposed 737 MAX safety upgrades.
Boeing shares were up 1.6% at $167.22 on Thursday afternoon, while Alaska Air stock was up 4.1% at $38.54.
Alaska Airlines already had ordered 37 of the jets before the grounding. If confirmed, a new order from such a major carrier would give Boeing's 737 MAX a sorely needed commercial boost as the U.S. planemaker tries to move beyond a crisis that has hammered its finances.
It would also mark a post-crisis test of the balance of power between Boeing and Airbus. The European planemaker is battling to keep a foothold in Alaska Airlines, which had operated an all-Boeing fleet until it acquired Virgin America in 2016.
However, any new deal between Alaska Airlines and Boeing is expected to include significant discounts given the MAX's woes and plunging demand for airplanes during the coronavirus crisis, industry sources said.
It was not immediately clear how many jets it may buy.
The talks are among several discussions Boeing is having with airlines, hoping to stimulate demand for the jet when it returns to the air. Analysts caution cutting prices too far could rattle some existing customers.
After months of delays, and pending approval of design and operational changes, Boeing expects to resume 737 MAX deliveries to airlines before year-end in the United States.
Seattle-based Alaska Airlines flies 166 older Boeing 737s and 71 Airbus A320-family aircraft.
It has one of the strongest balance sheets among U.S. airlines and analysts believe it could emerge from the pandemic crisis in a competitive position relative to its peers.
Boeing is also negotiating with Irish budget carrier Ryanair, one of its largest customers, over compensation for delays in MAX deliveries and a potential new order.
(Reporting by Eric M. Johnson in Seattle and Tracy Rucinski in Chicago; Editing by David Gregorio and Matthew Lewis)
By Eric M. Johnson and Tracy Rucinski