The deal, which the Times said is not yet finalized but in advanced negotiations, would feature the former president and first lady in programs. The shows would focus on "inspirational stories" about issues important to them.
CNN, also citing unnamed sources Thursday, said the talks center on a "production partnership."
The former president is no stranger to the streaming network. He appeared as a guest in the premiere episode of David Letterman's Netflix show, "My Next Guest Needs No Introduction." The streaming service also premiered a biopic on the former president in 2016, "Barry."
Though the Obamas have highly anticipated memoirs on the horizon and are active through the Obama Foundation, the Netflix deal would be the highest-profile media partnership for them since leaving the White House last year.
When the former first couple negotiated together to sell the rights to their forthcoming memoirs, they broke records when they nabbed a publishing deal for both books worth more than $60 million. A portion of the book advances would go to charity, including to the Obama Foundation.
Netflix declined to comment.