The initial investigation indicated it was due to a malfunction on the stall prevention system, a new feature on the MAX planes.
Several American pilots also reported issues with the MCAS and the Federal Aviation Administration said it ordered Boeing to issue a fix by April.
The aerospace giant held a conference call on Thursday with at least three carriers using the 737 MAX and gave them the fix, one source said, and the other airlines will get it early next week.
Contacted by AFP, Boeing declined to comment.
Boeing would like to start installing the patch in about 10 days, both sources said.
However, there is a question of logistics involving where the planes go for the installation.
American Airlines, which operates two dozen 737 MAX 8 aircraft, has chosen to update the software itself, one source told AFP.
Neither source was able to specify the cost of the upgrade, but one analyst estimated it would cost about $2 million for each plane for a total of less than $1 billion for the 371 planes in use currently.