The midfielder suffered the issue in a challenge with Pascal Struijk on the hour mark at Elland Road, which resulted in a red card for the home side’s defender.
Elliott was stretchered from the field and was taken to hospital, but later posted an image on his Instagram account with a thumbs up before the fixture had concluded.
Klopp told his post-match press conference: “First and foremost, it’s one of the few Instagram posts I love because if he sends that already then it shows he has not that much pain anymore, that’s great news.
"I think we all saw it, the ankle was not in the right place anymore. The medical department put it in the right place again, which is very important really in this moment that it goes quick. Apart from that, there is not a lot of good things to say about it.
“Obviously it’s a bad injury and we have to wait now for further examinations, assessments or whatever, scans, and that’s what we do.”