The Liverpool striker has been unavailable since sustaining a thigh injury in scoring against Bayern Munich in the Audi Cup on August 1.
Sturridge did not travel with the Reds squad for the Champions League qualifying play-off with Hoffenheim, but should be in contention when the Eagles visit Anfield this coming weekend.
“He is in a good way,” Klopp said at his pre-match press conference.
“We had a talk this morning and he was really close, he looked good yesterday. Two more sessions and he will be available for the weekend.”