Several people familiar with the Netflix discussions said that executives from Apple and Amazon, which have their own streaming services, have also expressed interest in talking with Mr. Obama about content deals.

The former president has maintained a low profile since leaving office. He and his wife are each writing highly anticipated memoirs, for which they were reportedly paid more than $60 million. And Mr. Obama has been paid hundreds of thousands of dollars for speeches in the United States and around the world. The Obamas are rarely seen in public in Washington, where they still live.

Mr. Obama has long expressed concerns about how the flow of information — and misinformation — has the power to shape public opinion. In the last several months, Mr. Obama has discussed with technology executives and wealthy investors the threats to American democracy from the manipulation of news.

He has seethed privately and publicly, about what he says is the manipulation of news by conservative outlets and the fractured delivery of information in the internet age. In several recent public appearances during the last several months, the former president hinted at his frustration with the way conservative news outlets have shaped people’s perceptions about the divisive 2016 campaign and the issues he cares about.

“If you watch Fox News, you are living on a different planet than you are if you are listening to NPR,” Mr. Obama told David Letterman in an interview broadcast in January for the comedian’s first Netflix program. Last December, at a forum in New Delhi, Mr. Obama conceded that “If I watch Fox News, I wouldn’t vote for me. I would watch it and say, ‘Who is that guy?’”

Evidence began to emerge while Mr. Obama was president that Facebook, Instagram, Twitter and YouTube were being used to spread false information about candidates and issues. Social media’s impact on society became even clearer last month, when the special counsel, Robert S. Mueller III, indicted 13 Russians and three companies that had used social media companies to undermine democracy in the United States and push voters to reject Hillary Clinton.