In an upcoming issue of PEOPLE, the actress — who will take on the role of Fanny Brice, originated by Barbra Streisand in 1964 — says she had the opportunity to watch Beanie Feldstein headline the musical and reached out to her after seeing it.
"I saw the show. I wrote her and told her what an incredible job I thought that she did," Michele, 36, shares. "I thought she was hilarious and beautiful and so wonderful. This is not an easy role, and she took it on with such bravery. And I wrote her and told her that."
Feldstein, 29, opened the musical when Funny Girl returned to the Great White Way in April. In July, the Booksmart actress announced that she would be leaving the production earlier than expected at the end of that month; the next day Michele was announced to be its new headliner.
The production later clarified in an exclusive statement to PEOPLE that they were "not blindsided" by Feldstein's post revealing that her final performance would be July 31.
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"I think that everybody just thinks everything is so drama-filled," Michele tells PEOPLE. "I also think that people really love the excitement of pitting women against each other, which I think is really sad and unfortunate."
The Glee alum says that she realizes stepping into the shoes of vaudeville comedian Fanny Brice is an "important opportunity," adding that she looks "to not only do a great job onstage every night, but do a great job offstage every single day, to be there for the cast and to be a leader."
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She adds, "That's something that I've really learned the importance of, especially over the past couple of years."
Michele says that she's never "felt more ready" to take on the role of Fanny Brice than she does now. Around 2014, there was talk that she would be the first actress to play the character since Streisand, 80, but that production never came to fruition.
"I had sort of let it go," she says, adding that she was "really young" during her time on Glee and that "there was a lot going on for me personally in my life."
She admits, "I didn't feel like I could do the show or the role justice, just on a television hiatus. You have to invest yourself into this process."
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"It wasn't until I stood on the stage at the Imperial Theatre in November at the Spring Awakening reunion that I turned to Jonathan after that night, and I was like, 'I really feel like I just want to do this again.' I have been in the television world for really 15 years, but it was in that moment where I just was like, 'This is my home,' " she says.
"I moved back to New York with my family, and that's when I really just started to get the itch to be back here and to be back on stage. And when this opportunity came my way, I jumped on it. I never felt more ready in my life to play Fanny Brice with the experiences, everything I've gone through in my life. Being 36, being a mother and a wife, I feel like I'm ready for this now."