Speaking with Andy Cohen on SiriusXM's Radio Andy Wednesday, Feldstein said that she didn't understand why Michele's name started trending on Twitter after it was announced in August that she was cast in Funny Girl.
"Has there been any correspondence between you guys yet?" Cohen, 53, asked the Impeachment: American Crime Story star, 28.
"I didn't know that any of this was happening by the way. And all of a sudden people started explaining it to me, and I was like: Wait, what's happening?" Feldstein said of the online hubbub.
"She very sweetly wrote on my Instagram. I don't know the woman whatsoever, but..." Feldstein said as Cohen cut in to call it a "happy" interaction.
getty (2) Beanie Feldstein, Lea Michele
Michele, who performed several Funny Girl songs on Glee and has previously expressed an interest in taking on the role of Fanny Brice on Broadway, indeed commented on Feldstein's Aug. 12 Instagram post sharing the news of her casting.
"Yes! YOU are the greatest star!" Michele, 35, wrote. "This is going to be epic!!"
In 2017, Michele responded to a fan question on Watch What Happens Live with Andy Cohen about the possibility of her headlining a Broadway production of Funny Girl after Ryan Murphy acquired the rights to mount a revival.
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"I hope so, I really hope so," she said at the time. "We were thinking of doing it right after Glee but I did a lot of the songs from Funny Girl on Glee so it felt like a little soon, but I feel really ready to do it now so maybe we could do it soon."
A source told PEOPLE in August that Michele had ultimately turned down the role when Murphy was involved in a potential revival. Michael Mayer, who directed Michele in Spring Awakening, has since obtained the rights and wanted to take the character in a "different direction," the source said.
"Lea has always supported his creative thoughts and thinks Beanie is the perfect person for the production," they added.
Feldstein's turn as Fanny Brice will mark the show's return to Broadway for the first time since 1964, when Barbra Streisand was in the lead role.
"I went to my third birthday party dressed as fanny brice so sometimes dreams actually come true 🥺🥺🥺," Feldstein wrote on Instagram in August of her casting.
In her chat with Cohen Wednesday, she added, "I certainly feel like it was my earliest dream [to play Fanny]. I truly can say it has been my dream my entire life. Like, from the moment I understood how to dream for something, it was this."