The blockbuster's director, Jennifer Lee, tells PEOPLE it's her "dream" to get Gad in an Olaf suit

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With the global box office for Disney’s Frozen sledding well beyond $1 billion in ticket sales (making it the fifth highest-grossing film of all time), you can bet execs aren’t planning to “Let it Go” anytime soon when it comes to their relationships with the film’s leading voice talents – Idina Menzel (Elsa), Kristen Bell (Anna), Jonathan Groff (Kristoff) and Josh Gad (Olaf the Snowman).

While the studio would probably have a difficult time persuading the cast to reprise their roles as costumed characters at Disneyland or in a story arc being planned for this fall on ABC’s Once Upon A Time, Frozen‘s writer/director Jennifer Lee is hopeful at least one the film’s actors will take part in her currently in-development Broadway musical adaptation.

Lee tells PEOPLE it is “my dream” to see Gad on stage singing, dancing and melting as Olaf.

“We need to all encourage him to get into a giant snowman suit to get comfortable with [it],” she says.

The in-demand actor, who collected a Tony nomination in 2011 for his breakout role in The Book of Mormon, has not ruled out the idea, Lee insists.

The writer/director was honored at Wednesday night’s Women in Film’s Crystal + Lucy Awards with the Dorothy Arzner Directors Award, alongside fellow honorees Cate Blanchett, Kerry Washington, Rose Byrne and Eva Longoria.

Though Frozen: The Musical doesn’t have an opening date, Lee has already ordered up additional songs to help tell the tale.

“Our goal is we want to do something new that transcends the film and becomes its own thing. There’s a potential to do something grander. It is a cold story, but we have to find some warmth.”

Could that possibly entail cranking down the temperature in the theater and distributing wool hats and mittens? “I hadn’t thought of that,” Lee says. “But I like that. You’ve got me thinking.”

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