The couple would make exclusive content for the USA streaming site focused on uplifting stories, the paper suggested.
One of the next places you see Barack Obama could be on Netflix.
Netflix told the BBC it had no comment to make about the reports. The Obamas' senior advisor, Eric Schultz, said the couple believes in the power of storytelling.
Obama will not use his Netflix shows to respond to United States president Donald Trump or conservative critics, and has instead talked about producing shows highlighting inspirational stories, the NYT said.
One possible show idea proposed that Obama could moderate talks focusing on issues that dominated his presidency, such as, health care, immigration, foreign policy and climate change, the newspaper said.
The specific amount that Barack and Michelle would receive has not yet been specified as well, but it would not be entirely surprising if they were offered a multi-million dollar deal in order to get the show, or shows, done for Netflix. "As they consider their future personal plans, they continue to explore new ways help others tell and share their stories".
And it has been investing heavily in content as it tries to grow that subscriber base - with hit shows such as Stranger Things and Black Mirror as well as films and documentaries.
The negotiations between the Obamas and Netflix are now serious, but they have not yet decided on the nature and format of the shows, nor how many episodes and seasons would there be.
Mr Obama already connects directly to an audience through social media.