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The two actors were spotted picking up some household items together while in upstate New York earlier this week. Tatum, 41, pushed the cart while Kravitz, 32, carried two bunches of flowers as they exited the store.
The pair have been seen spending time together in New York City multiple times in recent weeks — last Thursday, they were spotted making each other laugh while enjoying iced coffees. Days prior to that outing, Kravitz was photographed with her arms around Tatum's shoulders as she stood on the back pegs of his BMX bike.
Kravitz and Tatum are set to work together on her directorial debut Pussy Island, a thriller starring the Magic Mike actor as tech mogul Slater King who whisks away cocktail waitress Frida to his mysterious private island. The duo has also previously worked together on 2017's The Lego Batman Movie, voicing Clark Kent (Tatum) and Cat Woman (Kravitz).
getty (2) Channing Tatum; Zoë Kravitz
After romantic speculation surrounded the two at the beginning of this year, a source told PEOPLE the pair were not dating.
In June, Kravitz told Deadline that Tatum was her "first choice" and the actor she "thought of when [she] wrote this character" for the film, which will be produced by Kravitz, Tiffany Persons, Bruce Cohen, and Tatum's Free Association company.
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"I just knew from Magic Mike and his live shows, I got the sense he's a true feminist and I wanted to collaborate with someone who was clearly interested in exploring this subject matter," she explained.
Meanwhile, Tatum said he was "shocked" that Kravitz called him seemingly "out of nowhere," as they didn't know each other and he wasn't aware she was looking to direct. But he was grateful for the "chance to play a role like this," which is different from anything he has done before.
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"It was scary and liberating, just to be able to have a free conversation, where I was allowed to mess up, and say the wrong things," he said. "It became less about men and women and on more of a human thing that will open people's eyes, rather than us drawing lines in the sand, the you're a man, I'm a woman, it's [an] us-against-you thing. This goes deeper in a direction I'm fascinated by and I'm interested in seeing how people receive this and break it down in their own lives. And what they think the movie means and how would they have made decisions."