Despite Disney's new musical prequel Mufasa: The Lion King featuring original songs from Miranda, 44, the two actors reprising their roles as Pumbaa and Timon from the 2019 photorealistic Lion King remake don't get to join the singing action.
"Lin-Manuel Miranda had the audacity not to write us a song. And we are furious," Eichner, 46, jokingly tells PEOPLE. "We were wanting to get a song in the movie."
"I'm as good a singer as The Rock," protests Rogen, 42, referring to Dwayne Johnson singing Miranda's tunes in 2016's Moana. "That I will attest, that I maintain. So if The Rock's getting multiple Lin-Manuel songs, I can get one."
"I agree," says Eichner. "But we did manage a little musical moment."
As in the 1994 animated original (when they were voiced by Nathan Lane and Ernie Sabella) and 2019 remake, Timon and Pumbaa are a wisecracking duo in Mufasa, listening to and interrupting the tale of the titular lion from John Kani's mandrill Rafiki. They're joined by Mufasa's granddaughter Kiara -- played by Blue Ivy Carter, whose lioness cub is the daughter of her real-life mother Beyoncé's Nala and Donald Glover's Simba.
"We improvised so much and a shocking amount of that ad libbing gets into the movie and then gets animated," explains Eichner. Timon and Pumbaa's impromptu duet, he adds, was one such moment.
"We improvised our own song," says Rogen, quipping, "which I think Lin is going to take credit for."
"I know," says Eichner, joking that Miranda will "probably submit that for the Academy Awards. And then win based on our lyrics."
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Singing Miranda's songs in the musical prequel are Aaron Pierre, Kelvin Harrison Jr., Tiffany Boone, Anika Noni Rose, Keith David and more. While he and Rogen may not have gotten a moment at the level of "Can You Feel the Love Tonight?" Eichner says he's proud of the comedic duo's "spontaneity" together in the voiceover booth, "which is pretty rare in this big epic Disney family movie. To have that type of kind of raw improv make it to the screen is pretty unusual."
Mufasa: The Lion King is in theaters Dec. 20. Directed by Barry Jenkins and written by Jeff Nathanson, it stars Pierre as Mufasa and Harrison as Taka a.k.a. Scar.