According to Hollywoodlife, Followill drinks to excess in order to combat stage fright before going on stage, an issue which eventually led to the band's decision to cancel their entire US tour.
"I think all of this does have to do with Caleb's alcoholism. He suffers from extreme anxiety and has a hard time standing in front of crowds, which is why it's so ironic he's become one of the world's largest rock stars," an insider told the website.
"There's a running joke in the band that Caleb can't go on stage without having a cocktail first."
Kings of Leon were forced to end a recent concert in Houston, Texas early after Caleb walked off stage complaining about the heat and refused to return.
The group later planned to reschedule the gig before the announcement of the tour cancellation.
Caleb's brother Jared Followill tweeted on Monday: "I love our fans so much. I know you guys aren't stupid. I can't lie. There are problems in our band bigger than not drinking enough Gatorade."
Drummer Nathan Followill added: "Not so good morning for me today. Ashamed & embarrassed by last night's fiasco. Can't apologise enough, utterly gutted. A million I'm sorry's."