In an AEW media call today, Cody Rhodes discussed Jeff Cobb's status with the company:

"It’s still in gestation. Jeff works with New Japan, he works with Ring Of Honor and now he works with AEW. I’m a big fan of Jeff Cobb because I like shooters in wrestling. I don’t try to consider myself one with my limited amateur background, but I think Jeff is a really, he’s a tank. He’s a special athlete.

So I think honestly, to be transparent with you, it’s in gestation. I would hope that he maybe pursue the longer [tenure] with AEW but I don’t want it to impede on anything he’s doing in his soul, if that makes sense. If he wants to travel the globe and do all kinds of stuff, have at it.

That’s one of the great things about AEW, there’s no blanket contracts. Everybody’s contract is different about what they can do, where they can go, and Tony Khan has tailored and contoured contracts to speak to your sensibility. ‘Hey, if this independent means a lot to me’ or ‘going to Wrestle Kingdom means a lot to me,’ whatever it may be, it’s door’s open and we’re open for business. But Jeff, I’m sorry, I’ll just have to keep it vague with him as well because honestly, we don’t know just yet.

We do have Jeff for more than just the Atlanta show, but I’d love to see Jeff in a more long-term deal with us. He’s a special talent."

Transcript WrestleZone.com.