Firmino scored 27 goals and 17 assists in its best season for the Reds last semester.
But the striker has scored only four goals so far this season and only one in each of the past nine matches.
The Brazilian was largely uninvolved in a 1-1 draw with Arsenal on the weekend, despite scoring the post with a try.
The 27-year-old has as many goals in the Champions League as in the Premier League, two out of three in Europe.
And thus he should take his place for a continental duel with Red Star Belgrade in Serbia – Firmino has played in all 31 European games since October 2015 under Klopp.
However, the resurrection of Daniel Sturridge since the preseason means that Firmino's starring role is far from guaranteed. The England international has also scored four goals, although he only had one-third of the minutes of Klopp's 9-game season.
The German manager insists, however, that Firmino's abusive start does not bother too much.
When asked if he was worried about the striker, Klopp told reporters: "No. He works hard, sometimes better, sometimes a little less, but good. That's the way it is.
"Everything will be alright. If he did not score in the last games, then … [the last] nine? All competitions?
"Did not he hit Red Star? That was the only goal he scored? OK Good.
"I'm not worried, this happens, he's a very important player for us.
"I was not happy with our first half [against Arsenal] in London and he was involved. That's what I'm talking about.
"In the end everything will be fine. We know these situations.
"Sometimes clicking is easier than at other moments, that's all. There are no concerns. "
Former Chelsea and Celtic striker Tony Cascarino wrote in his weekly column for The Times that he believes Firmino would benefit from a team spell.
He said: "Roberto Firmino looks to me like he needs a break, and I would not be surprised if Jürgen Klopp eliminated him from one of the next matches.
"He's a wonderful player, but he has scored once in the last nine appearances for Liverpool – against Red Star Belgrade – and not a single assist.
"He has played in 69 games since the beginning of last season, more than any other Premier League player." Even Mo Salah has played two games less.
"Some players are less responsive to more competition for their seats and I wonder if Firmino is one of them.
"Daniel Sturridge, Xherdan Shaqiri and Adam Lallana are challenging him to a place in the team right now, which may have made Firmino less comfortable."
And Klopp also acknowledged that the workload of Firmino is a constant concern for him and his employees.
When asked if he felt the South American frontman was tired, he said, "Not really, but of course we think about 100%. Actually, constantly.
"It often leads to the decision that he still has to play. It starts or comes, sometimes it's better to come into play later, when the rest is a bit tired, but we'll see how we handle it. "