The proposed deal was reported Friday by The New York Times, which cited people familiar with the discussions who were not identified.
The deal followed a heated auction for global rights to the two books with bidding that reached more than $60 million, a record sum for US presidential memoirs, the Financial Times had reported past year. Notably, the report claims that the show could focus on "inspirational stories" or, just as easily, hot takes on whatever happens to be the pertinent political issue of the week.
Another show would involve Michelle and could feature topics that she championed during her time as the first lady.
If confirmed, the deal would give a global platform for the Obamas, bypassing mainstream United States media such as Fox News.
The format could include talk-show-style or documentary productions.
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The police official further said that until the investigation is done, police can not reveal the names of the people involved.
Netflix is available in some 200 markets worldwide and produces programs in several languages.
With rumors that Apple and Amazon have also tried to engage with Barack Obama and make a deal, there's a lot of competition for the former president to sign with a streaming service and provide them with exclusive content.
Netflix did not respond for a request for comment.
Netflix told the BBC it had no comment to make about the reports.
"President and Mrs. Obama have always believed in the power of storytelling to inspire", Eric Schultz, a senior adviser to the former president told The New York Times. "As they consider their future personal plans, they continue to explore new ways help others tell and share their stories".