Oxlade-Chamberlain is yet to feature since the 3-1 win over Newcastle at the end of last season, having suffered a knee injury during pre-season training.
It was a big blow for the 27-year-old, who had recovered from a serious knee problem in 2018 to make 43 appearances last term, forcing him back onto the treatment table and, later, the gym at Kirkby.
Ahead of the Reds’ 1-1 draw with Midtjylland, Oxlade-Chamberlain joined the squad for full training, but he was not included for the trip to Denmark.
“Oxlade is in normal training – [he has been] doing parts of training now for a week or so,” he told reporters on Friday.
“He is now in full training and we will see.
“The situation probably demands to involve him as soon as possible, but I don’t know if the weekend is that moment already.”
Klopp was asked to reflect further on the situation for Oxlade-Chamberlain, and said that while he “will not rush it,” he will “immediately” be an option when he has trained for long enough.
“It’s long, eh? Unbelievable. I still remember the situation how it happened in training, normal challenge and one gets up, the other not,” the manager added.
“That’s really hard. Tough time for him, but the sun shines for him already for a month or two, since he’s doing all the necessary stuff in rehab.
“He was on the pitch with the ball, now he’s with the team. So all these steps, it’s great for him, great for us.
“Again, we cannot and will not rush it. But when he’s long enough in normal team training, then of course he becomes an option immediately.
“It’s good, absolutely good.”