Elliott was back in full training at Kirkby earlier in the week, and was welcomed onto the pitch with a trademark hug from his manager.
It came after four months out with an ankle injury that required surgery, with the youngster praised for his attitude in recovery as he worked towards his comeback.
Assistant manager Pepijn Lijnders hailed Elliott’s performance in training ahead of the League Cup semi-final clash at Arsenal, but insisted that Klopp and his staff had forced themselves to be patient.
“It’s outstanding,” he said of Elliott’s return.
“I have a really nice office with a really good view of the pitches, and when Harvey did his rehab sessions in the last weeks I could watch them, probably five of them, so I got already excited about watching them.
“Then he came back, so it’s really cool.
“He was out for a long time, so we cannot and will not and should not rush it, but he looked directly like he could play!
“We had to force ourselves a little bit, to say ‘no, that makes no sense’ after a long period.
“But I’m pretty sure after the international break he should be ready.”
If he is back as expected, Elliott could be involved for the FA Cup fourth-round tie at home to Cardiff, which could give him an opportunity to build minutes against a Championship side.