The Brazilian was forced off midway through the first half of the Villa Park clash with what appeared to be a hamstring problem.
Klopp’s men are level on points with City, who travel to Wolves this evening.
Liverpool await further news on Fabinho’s issue.
Meanwhile, Klopp confirmed that Andy Robertson was rested against Villa, having been omitted from the match-day squad.
The Reds boss said: “I don’t know [how bad it is]. He felt the muscle, not too much.
“He is quite positive but I’m not sure what I can make of that, to be honest. We will see.
“I think the rest came through without problems.
“Robbo was not in the squad today because I wanted to give him just a rest at home and bring another striker into the squad if we needed, that’s it.
“Apart from that, we should be fine.
“He [Fabinho] has a good feeling and that gives me a better feeling than I had and I took him off. What that means, I don’t know yet.”