Are Timothée Chalamet and Lily-Rose Depp Dating?

Timothée Chalamet and Lily-Rose Depp might be Hollywood’s newest couple.

The Call Me by Your Name leading man, 22, and the actress/model, 19, appear to be getting close after meeting while filming the upcoming Netflix drama The King together.

Fan accounts on social media have linked Chalamet and Depp, the daughter of Johnny Depp and his ex Vanessa Paradis, pointing to photos of the pair together as evidence. Reps for Chalamet and Depp have not responded to PEOPLE’s requests for comment.

In photos of the Oscar-nominated actor and Depp that surfaced on Instagram, the casually dressed stars are seen together in Central Park and at Mud Coffee in New York City. In one picture, Depp seemed to put her arm around Chalamet.

Chalamet and Depp follow each other on Instagram and both attended the Toronto International Film Festival in September.

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Chalamet — whose next film, Beautiful Boy, is already getting awards buzz — dated Madonna‘s daughter Lourdes Leon, 21, when they were students at La Guardia High School of Music & Art and Performing Arts.

In 2017, Chalamet seemed to be on good terms with his ex. “She hasn’t seen [Call Me by Your Name] yet, but she’s excited to. She teases me about it,” he said on Andy Cohen‘s SiriusXM show. “The movie itself she’s very excited about. … It’s the public appearance stuff around it, some of the late-night things I’ve done, I get made fun of.”

Depp was previously in a relationship with Ash Stymest. Depp’s dad marveled at her adult status on The Ellen DeGeneres Show in 2017. “She’s growing up,” he said. “It’s incredible. It happened very quickly and she’s a woman … sort of.”

“That freaks a dad out,” he continued. “But she handles it so well, she’s so grounded and very cool about it.”