The 67-year-old director was at the eatery with his wife Kate Capshaw, stepdaughter Jessica Capshaw and some of his staffers when Swift arrived with an entourage, reported the New York Post.
The restaurant's staff put two tables together to accommodate the group.
"Taylor and Steven were in deep conversation the whole time," a source said.
Swift, 24, recently filmed 'The Giver' for the Weinstein Company, co-starring Meryl Streep, Katie Holmes and Jeff Bridges.
Spielberg had previously met Swift, 24, at a Beverly Hills charity gala.
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