However Koetter, according to FOXSports.com, has since signed a contract extension to stay with the Falcons through the 2013 season.
The Chiefs also reportedly interviewed Falcons special teams coach Keith Armstrong on Tuesday, which would have satisfied the NFL's "Rooney Rule," which requires at least one minority candidate to be considered for each head-coaching opening.
The Chiefs have not confirmed any reported interviews.
Reid, according to USA Today, also is scheduled to meet with the Cardinals in Arizona on Thursday. It had been reported Tuesday by multiple media outlets that Reid was virtually a slam dunk to become the next Cardinals coach.
But Arizona vice president of media relations Mark Dalton has since tweeted, "I'm 99% sure that reports of a deal being 95% done are 100% incorrect."
Hunt also indicated on Monday that he would be interested in interviewing former NFL head coaches, present college head coaches and present NFL coordinators.
Two coordinator names that may surface in the coming days or weeks are New Orleans Saints offensive coordinator Pete Carmichael, Jr., and St. Louis Rams offensive coordinator Brian Schottenheimer.
Hunt has sought advice from former Chiefs coach Marty Schottenheimer in the past few months, which could mean someone from Schottenhiemer's coaching tree could get an interview.
Carmichael worked for Schottenheimer for one season with the Washington Redskins in 2001, and also spent four seasons on Schottenheimer's staff in San Diego before joining Sean Payton with the Saints.
Brian Schottenheimer worked with his father in Kansas City, Washington and San Diego, where he served as Drew Brees' quarterbacks coach.
Rams head coach Jeff Fisher said last month he believes Brian is ready to take the next step in coaching.
"He's ready to handle the job and he's capable," Fisher told reporters in St. Louis. "I think he'd do a great job at it. Certainly, he's been around the game for a long time. He's got a great pedigree, and this is the time of the year when people start throwing names out there."