Liverpool will still be without first-choice goalkeeper Alisson for a few more games.
The Reds will travel to Goodison Park for the first Merseyside derby of the season.
Both Sadio Mane and Thiago Alcantara will be unavailable for contention after the duo tested positive for the coronavirus.
Naby Keita will also be out after a reported coronavirus outbreak within the Guinea squad.
Klopp told his pre-match press conference: “[It’s] very, very positive with Ali, it looks really good. [He’s] made big steps. I don’t have a timeframe, but it looks really good.
“That’s it, pretty much. Naby will not be ready. Apart from that, long-term of course, Oxlade-Chamberlain is not and so on, but they all came back healthy from the internationals.”
On Thiago and Mane after they tested positive for Covid-19 before the international break: “We all learn on a daily basis about it. They are in training for five or six days [now].
“Then, of course, we assess that every day. We have our specific measurements, how we do it with heart rate and how we can measure if they are more fatigued than usual and stuff like this.
“They both looked really good, to be honest. We are very close with the doctors and we don’t want to – and would never – risk anybody.
“Usually in these cases, in at least the last three, four of five days of the quarantine the boys are already ready. They cannot come out of quarantine, but they are on treadmills, on the bike and these kind of things so when they start training again it is not that they start from nil. They have still a proper shape, so it should be fine.
See More: Liverpool FC Fixtures 2020/21