Obama and the Oscar-winner were at upscale seafood eatery Marea, spies said.
"Spielberg walked through the front and no one noticed," said the source, while Obama arrived through a side entrance.
"They were with a group — with lots of Secret Service," said the source. "But it was still pretty low-key with no disruptions to other diners."
The Obamas have seven planned Netflix projects via their Higher Ground Productions, including an adaptation of David W. Blight's 2018 Pulitzer Prize-winning book, "Frederick Douglass: Prophet of Freedom," as well as a series called "Bloom," set in the fashion world of New York after WWII.
In 2015, it was reported that Spielberg — whom Obama awarded a Medal of Freedom the same year — was helping the ex-pol create a "narrative" for post-presidential life.