Crosby ran the bases Saturday and came out of it well, so he'll be activated the same day he's available to come off the DL.
"He's fine," Geren said. "He's doing great. It looks like he'll be ready to join us when his DL term comes to a close."
Crosby is not expected to play in rehab games to get ready for his return. He has been taking batting practice instead, and his calf hasn't hindered his swing.
"He doesn't feel like he needs to [go on a rehab assignment], and feels really good swinging the bat," Geren said. "As of yesterday, he didn't feel like he needed to or wanted to."
In a game against the Yankees on Aug. 17, Crosby exited in the sixth inning with tightness in his left calf.
Before the injury, Crosby was batting .223 with six home runs and 27 RBIs in 87 games, while playing first base, third base, second base and right field.
Rhett Bollinger is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.