Young explained the story behind the song in an interview with The Boot
"I had been in LA visiting family and friends, listening to pop radio, and I heard all these songs in a row about a dude trying to sleep with a girl. I thought, "There has to be a sweet twist on that subject, somehow." I just started thinking about, my last relationship was six years. We never lived together, but we always did the goodnight phone call or text. When that becomes a habit, you find yourself restless, trying to go to sleep without the goodnight phone call or text.
I thought that was way sweeter than 'let's get busy.' I brought [Ebach and Archer] the idea for 'Sleep Without You,"' and it was a quick write. And, it was my first write with either of them, so that doesn't usually happen; normally there's, like, a feeling-out process with new writers. It just happened really quick and easy.
We left the write, and about two hours later, Justin sent a completely finished demo. We wrote it, he put down the guitar, and I sang it, and I left, so all I knew was the guitar vocal. He sent it pretty close to how it sounded on the radio. Kelly wrote that night, 'I'm not embarrassed to admit that I'm dancing around the kitchen now.'"