According to a report on SI.com, Davis was claimed off waivers by the Brewers within the last day. The teams have 48 hours from the time of the claim to work out a trade.
Davis said he heard reports of the Brewers' claim Wednesday night, but he had not received an official word from either team. A free agent at the end of the season, Davis said he is seeking a long-term deal.
"Going back to Milwaukee would be fun," he said. "I know the fans would be behind me."
D-backs general manager Josh Byrnes declined to comment on any facet of the waiver process. It's Brewers general manager Doug Melvin's policy not to comment on players going through the waiver process.
Placing a player on waivers in August is a common practice. Most teams, in fact, put their entire rosters through the process.
If Davis was claimed, the D-backs would have three choices. They could work out a trade with the claiming team, they could pull Davis back off waivers or they could just let the claiming team assume his contract without completing a trade.
"It's a win-win situation," Davis said of the possibility of being dealt. "I go to a team that's probably contending, this team gets something they probably need and I still become a free agent at the end of the year and can possibly come back here."
Pitching in the playoffs is a big carrot for the pitcher in the final year of his contract.
"I could get a couple of starts in the playoffs and you're one game away from a huge contract," he said. "That's pretty much what it is. You hit a big home run and you pretty much play for the rest of your career based on that one home run. Just that one big game, you end up showing you could get that big hit or pitch a big game."
When the non-waiver Deadline was approaching, Davis felt some anxiety because he had some plans set with his children in Arizona for the summer. Now, though, with those events having passed, the uncertainty does not bother him.
"It's something that's out of my control, so there's no reason to stress about it -- especially this late in the year," Davis said.
As for whether the D-backs would sign him to a contract extension before the end of the season, Davis did not sound optimistic.
"I very much doubt it," he said.
Steve Gilbert is a reporter for MLB.com. Jesse Sanchez contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.