The band offered Daughtry a job Thursday, hours after viewers voted him off the Fox television talent show.
Bass player Jeff Abercrombie and guitarist Carl Bell made their pitch on the TV show "Extra."
"Chris, if you are watching, we've talked about this before, and if you want to entertain it again we'll take it and go," Abercrombie said.
Daughtry, who dreamed of becoming a rock star while working in the service department at a Greensboro car dealership, told reporters earlier Thursday he was considering whether to pursue fronting an established rock band or launching a solo career.
"I'm a songwriter myself," the 26-year-old said. "To be able to launch my own career would be a dream" come true.
The buzz around Daughtry for weeks has been that he could end up Fuel's lead singer; Scallions left the band in February.
Daughtry performed the band's song "Hemorrhage" on a recent "Idol" show. His wife, Deanna, said she's not sure which option he should pursue, but either way music is all he's ever wanted to do.
"He's got a lot on him and hopefully he'll have a lot of wisdom there," she said. "The public forgets so fast about those idols once they get off the show. I just hope they don't forget about Chris."
Many observers thought the shaved-head rocker from McLeansville would win this year's competition.
On Tuesday's show, Daughtry performed two Elvis Presley songs. His rendition of "Suspicious Minds" drew strong reviews from judges. Paula Abdul said, "See you in the finals."
Judge Simon Cowell said his second song — "A Little Less Conversation" — was "flat" and not as good as the first performance.
Daughtry, who said he doesn't regret anything he did on the show, said he was shocked to get voted off because so many people had picked him to win — which may have led overconfident fans to not bother casting votes.
"They didn't have to vote as hard, and I think that was the downfall, in my opinion," he said, refusing to critique the other three finalists. "It was definitely a gut-wrenching moment and I was not expecting it, even a little bit."
Some fans around his hometown fear their votes were mistakenly credited to one of the other contestants because they'd get another hopeful's voice thanking them for the call instead of Daughtry's, family friend Tracey Adams said.
One music industry expert said it shouldn't be the end for Daughtry, who has a great opportunity to cash in as a solo artist because of the equity he's built on the show.
"I think he should definitely pursue that at this point," said Jeff Walker, president of AristoMedia, a Nashville-based company that develops and promotes music artists. "He's got a lot of people that like him."