Carvalho was a highly anticipated arrival at Anfield following his breakout season with Fulham, but it has been a stop-start campaign so far.
His next goal for the club came in the Carabao Cup defeat to Man City on December 22, but he was then withdrawn at half-time in that game and has not featured since.
Asked for an explanation for Carvalho going five games now as an unused substitute, Klopp insisted that it was not a “personal” issue.
“There are no, from my point of view, personal situations or stuff like this,” he told reporters.
“We are a football team, players offer and I have to pick. That’s pretty much everything. There’s nothing else.
“He’s behaving well, everything is good, didn’t have any problems or whatever. It’s just sports decisions that you make for the moment.
“But we are working, he is working. That’s all.”
There is no guarantee, of course, but the No. 28 is a viable candidate along with those who started the 3-0 loss at Brighton on Saturday.
That humiliation at the Amex has led to question marks over the strength of the squad, not least in their mentality, but Klopp is adamant that there are no fractures developing.
“It’s always the question. What is there first: team spirit or success? I am 100 percent it is always the spirit first,” he said.
“Maybe there are some examples where it was different – I was never involved in them.
“But there’s nothing. There are no issues or whatever. The boys are good with each other, we are good with each other.
“That doesn’t mean that I cannot be harsh. That doesn’t that they cannot be clear in what they want from each other.
“All these things happen. It’s clear.
“Thank god nothing like that happens outside of the dressing room. That would be probably really bad if then all of a sudden we had to explain these kinds of things.
“So far we are at least good with that. But we are very clear with ourselves. We don’t hide, neither information nor ourselves.
“So that’s it, but we have to admit too often this season we didn’t play to our potential. That’s the truth as well.”