Singer Brian Littrell reveals Trump's aides approached him and asked if he and his bandmates would be interested, and he assured them he'd ask.
"It just didn't work out," he tells TMZ. "I would've been there if I could've, but we're starting rehearsals for our (Las) Vegas show. So it's like it just couldn't happen."
But Brian insists the decision not to play wasn't a snub, and he urges his fellow celebrities to stop criticising Trump and give the new leader a chance.
"Hollywood needs to chill out," the pop star says. "You're talking about the Commander-in-Chief. We're talking about respect.
"This guy, as of Friday, Inauguration Day, he's gonna be our President. He's gonna be our Commander-in-Chief. And he's gonna do so many great things, in my opinion. I have faith in the system. I have faith in his character, his beliefs, and his balls - let's just put it that way."
Trump's inauguration ball organisers have struggled to book top performers and Elton John, Charlotte Church, and Rebecca Ferguson reportedly turned down invitations, while Jennifer Holliday pulled out of a pre-inauguration event after she was criticised for signing on.
The ball will feature performances from Jackie Evancho, Chrisette Michele, the Mormon Tabernacle Choir and dancers The Rockettes.