Oxlade-Chamberlain has not featured since April after suffering an injury against Roma in the first leg of the Champions League semi-final.
But Klopp now says the 25-year-old is likely to feature before the end of the campaign, while Rhian Brewster will remain sidelined for the foreseeable future.
“He’s outside running and is in a good way,” he said of the 18-year-old. “But we don’t have to think about him before pre-season.
“Alex is closer, last time I put a bit of pressure on the medical department. He looks without any problems, no swelling.
“I think you’ll see him this season.”