Davis sustained a torn meniscus on a swinging strikeout May 30 against the D-backs and had surgery June 2. He is in the fifth week of a rehabilitation originally projected to take 4-6 weeks.
"We saw him run today; he ran good. We saw him throw yesterday; he threw good," Brewers manager Craig Counsell said. "All signs are very positive for Chris. … We're getting close with him, for sure. Once you're in the cage, you're running, you're throwing, the next step is playing."
Before Wednesday, Davis had been limited to controlled swings in the batting cage and agility drills in the outfield. If he responds well to full batting practice, and passes baserunning tests in the coming days, Davis will be assigned to a Minor League affiliate to continue his comeback.
For reference, when catcher Jonathan Lucroy was sidelined more than a month by a fractured left toe earlier this season, he played only four games at Class A Advanced Brevard County before rejoining the Brewers.
"We haven't talked about a date yet [for Davis]," Counsell said. "I would say it's similar to Lucroy. I don't think it's much different than that. Four, five, six games."
Davis ranks third on the team with a .446 slugging percentage and .783 OPS. He is batting .250 with five home runs and 15 RBIs in 46 games.
The other injured Brewer, right-hander Wily Peralta, is still throwing on flat ground as he recovers from an oblique strain. Peralta could throw his first mound session later this week, Counsell said, but he would then have to slowly build up his pitch count.
Adam McCalvy is a reporter for MLB.com. Follow him on Twitter @AdamMcCalvy, like him on Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.