The report states that people in WWE believe that he is talking with AEW and that is his likely destination for an in-ring return. That has not been confirmed by Punk or AEW management and likely will never be confirmed by either party since they would want to keep the news of his signing top secret.
On the Wrestling Observer forum, Dave Meltzer talked about two major names that AEW hoped to get signed in June and those names are far bigger than Andrade El Idolo.
Meltzer said the following in regards to Punk: "They've been in talks but Tony talks to everyone. Anyway, I guess that explains first item in last week's AEW section [of the Wrestling Observer Newsletter]. Only thing I know is that in June there were two people far bigger than Andrade they were hopeful of getting but didn't have, and were hopeful of the announcement that month if they were finalized. The month ended."
Khan recently said during an interview that there are surprises coming that nobody but he knows about. The fact that he stated that the surprises are coming indicates that deals have been reached.
The other big name that has been speculated on is Daniel Bryan (Bryan Danielson). Bryan is no longer on WWE's internal roster and he is no longer being included for projects being worked on by WWE's partners.
If any of those two are signed, they can show up at any time but one would assume that Punk would be saved for All Out weekend in Chicago and perhaps they would want to save Bryan for AEW Dynamite: Grand Slam in New York City. Time will tell.