Davidson was forced into action Sunday when Cody Ross went down with an injury in the first inning and he pinch-hit in Monday's game.
"I want to keep him so he's playing, but at the same time I'm not just going to throw him in there and play him every day," manager Kirk Gibson said. "We have other guys in front of him."
Davidson could get starts at third if Martin Prado takes a day off or is used in left field or at second base. He will also take some grounders at first, a position he played at times in the Minors, and could see time there when Paul Goldschmidt gets a rare off-day.
"You tend to go more with your veteran guys right now at this point in the season," Gibson said. "At the same time, [we'll] try to work him into good situations."
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.