"It's just not where we want it to be, especially since I'm already on the DL and not just going to come off," Davidson said. "It hasn't been getting too much better right now, so we're going to re-evaluate the next couple days and then go from there.
"The good thing is the doctors say that one day you'll just kind of wake up and it'll be gone. We're kind of waiting for that and then we'll go from there."
Davidson suffered the injury when he was hit by a Marcus Stroman pitch on Aug. 1 against Toronto and departed early from the game. He continues to lead the team with 22 homers to go with 51 RBIs and a .500 slugging percentage in 88 games this season.
With Tuesday marking two weeks without on-field action, Davidson believes a rehab assignment with Triple-A Charlotte will precede his White Sox return.
"That's kind of a long way from live pitching," Davidson said. "I've been trying to get in with the pitchers here and stuff like that as much as I can but probably do that (at Charlotte) for a couple days and be back here.
"I can do pretty much everything except swing. I'm working out, running, taking ground balls and standing in on bullpens and stuff like that. Just trying to do as much as I can and doing some front-arm with my lead hand, hitting off the tee and flips. But that's about it."
The manner in which Davidson offered at the Stroman pitch in question exposed his wrist, leading to Davidson getting hit in the worst possible spot.
"But luckily everything's structurally good," Davidson said. "It's just the waiting game right now that's not very fun to deal with."
Scott Merkin has covered the White Sox for MLB.com since 2003. Read his blog, Merk's Works, follow him on Twitter @scottmerkin, on Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.