Doctor Who exec Steven Moffat announced this week that Gillan and her co-star Arthur Darvill will leave the sci-fi programme at some point during the seventh series.
Gillan expressed a desire to do more stage work once she leaves the role of Amy Pond behind for good.
"I want to do more theatre. I want to do more stage. I have a real passion for it," the actress told The Los Angeles Times. "I want to do it as much as screen stuff, in all honesty, so that would be really amazing."
She further explained: "Maybe something on Broadway. I'd love to do that. Not a musical, maybe like a play on Broadway.
"I genuinely just want to do good work. I'm interested in character, whether that's in a play or a film or an indie film."
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Gillan also revealed that she was thrilled to play model Jean Shrimpton in the television movie We'll Take Manhattan, which airs in the UK on BBC Four in January.
"I really didn't think that would happen. When I got offered that, I was like, 'Really?'" the star admitted. "She's actually watched it, and she loved it. That's all I wanted from that role. That's enough for me, that she was happy with what [we] did with it."
Doctor Who returns for the festive special 'The Doctor, the Widow and the Wardrobe' on Christmas Day on BBC One in the UK and on BBC America in the US.
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Watch a trailer for 'The Doctor, the Widow and the Wardrobe' below: