VIDEO : Ben Affleck and Sienna Miller Seen Holding Hands on Movie Set

Ben Affleck and Sienna Miller have the rumor mill turning! The duo was spotted holding hands while in between takes on the set of their new film, Live by Night, in Los Angeles earlier this week, causing people to question whether there may be something romantic brewing. The couple-y photos show Sienna in costume?decked out in accordance to the film's 1920s theme?holding tightly onto Ben's hand, who looked casual in street wear while directing on set. The photos appear pretty lovey-dovey, but don't start shipping the stars just yet. A source tells the E! News, "He is directing her and his movie?a movie in which he stars in. So while they not only share scenes, he directs her."