updated 11/04/2010 AT 12:00 PM ET
•originally published 11/04/2010 AT 1:40 PM ET
But was the duo’s dinner at New York City eatery The Lion more business than pleasure?
Sources tell PEOPLE that although Lively, 23, and DiCaprio, 35, were indeed sitting next to each other, they were not sitting alone.
The dinner “was with Baz [Luhrmann] and five other people,” a source says.