Childress said he hopes to have something to announce within the next few weeks.
"I hope we have it done in a couple of days," Bowyer said with a laugh as he prepared for Sunday's Brickyard 400 at Indianapolis Motor Speedway.
There has been speculation that Bowyer was waiting to see if Carl Edwards leaves Roush Fenway Racing for Joe Gibbs Racing, which would open a possible spot for him with Roush.
Prior to Red Bull Racing announcing last month it was leaving the sport, there were reports that Bowyer was headed to Red Bull.
Bowyer and Childress said they are committed to each other.
"He's committed he's going to race with us," Childress said. "Our whole deal is we've got to put the dollars together."
David Newton covers NASCAR for ESPN.com. He can be reached at firstname.lastname@example.org.