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Ben Affleck, Sienna Miller

HGVC / AKM-GSI

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."

Ben Affleck

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The insider adds, "He also directs others in this movie, [but] no one seems to be interested in those photos with him and his male costars."

Of course the pictures are only heightened by the fact that both actors separated from their significant others over the past year. Ben and Jennifer Garner announced their split in June after 10 years of marriage, while Sienna and Tom Sturridge decided to end their three-year engagement in July.

Despite their split, Ben has made a large effort to be with his family as much as possible.  In fact, our source notes that he has been seen "out with the family since he came back to shoot in L.A."

Prioritizing family is something both Ben and Jen expressed at the time of their split, releasing a statement to E! News, saying: "After much thought and careful consideration, we have made the difficult decision to divorce. We go forward with love and friendship for one another and a commitment to co-parenting our children whose privacy we ask to be respected during this difficult time."