Drew, who strained his left hamstring on April 17 in San Francisco, was placed on the disabled list on April 26 (retroactive to April 25).
Arizona manager Bob Melvin said he expected Drew to start an injury rehab stint Thursday in extended spring training, and after that to move to Triple-A Reno for a few games.
"If that's the case, we're probably looking latter part of the homestand," Melvin said, referring to when Drew could be activated.
The D-backs' upcoming homestand ends next Wednesday, so according to Melvin's timetable, Drew could be activated Tuesday or Wednesday.
Augie Ojeda has done a nice job filling in for Drew, hitting .240 with a .367 on-base percentage. Still, the D-backs are eager to have Drew back.
"Obviously, Stephen is one of our better offensive weapons and an all-around shortstop and I think one of the better shortstops in the league," Melvin said. "When you lose a player like that, you do lose something and we're looking forward to getting him back."
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.