The proposed deal was reported Friday by The New York Times, which cited people familiar with the discussions who were not identified.
The report sent shares to an all-time high of $326.74 earlier. The Los Gatos, California, company's stock reached $326.07 in afternoon trading, marking a gain of nearly 3 percent.
Netflix did not respond for a request for comment. Obama spokeswoman Katie Hill declined comment on the report.
Obama senior adviser Eric Schultz, in a statement provided to The Associated Press, said the Obamas believe in the power of storytelling to inspire.
Schultz said the couple continues to explore new ways to help others share their stories.
The New York Times reported that Obama doesn't intend to use his Netflix shows to respond directly to President Donald Trump or conservative critics.
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