Firmino netted 27 times, adding 17 assists, in his best ever season for the Reds last term.
But the forward has only four goals in 15 games so far this term and just one in his last nine games across all competitions.
The Brazilian was largely uninvolved against Arsenal in a 1-1 draw at the weekend, although he struck the post with one attempt.
The 27-year-old has as many goals in the Champions League as he does in the Premier League this term, with two in three in Europe.
And that is likely to see him keep his place for a crunch continental clash with Red Star Belgrade in Serbia tonight – with Firmino having played in all 31 of the European games Liverpool have played under Klopp since October 2015.
But Daniel Sturridge’s revival since pre-season means Firmino’s starting role is far from guaranteed, the England international having also managed four goals despite playing only a third of the minutes of Klopp’s go-to No 9.
Yet the German manager insists he is not overly bothered by Firmino’s misfiring start.
Asked if he was concerned about the striker, Klopp told reporters: “No. He’s hard-working, sometimes better, sometimes a bit less, but good. That’s how it is.
“It will be all fine for sure. If he didn’t score in the last few games then… one in [the last] nine? All competitions?
“Didn’t he score against Red Star? That was the one goal he scored? Okay, good.
“I am not concerned. Things like this happen. He is a very important player for us.
“I was not really happy with our defending first half [against Arsenal] in London and he was involved in that. That’s what I’m talking about.
“In the end everything will be fine. We know about these situations.
“Sometimes it is clicking easier than in 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 spell out of the team.
He said: “Roberto Firmino looks to me like he needs a rest and I wouldn’t be surprised to see Jurgen Klopp leave him out of one of the next few games.
“He’s a wonderful player but in the past nine of his appearances for Liverpool he has scored once – against Red Star Belgrade – and not managed a single assist.
“He’s played in 69 games since the start of last season, more than any other player in the Premier League. “Even Mo Salah has played two fewer. He would benefit from a break to freshen him up.
“Some players react less well to more competition for their place and I wonder whether Firmino is one of those.
“Daniel Sturridge, Xherdan Shaqiri and Adam Lallana are all challenging him for places in the team at the moment and that may have made Firmino less comfortable.”
And Klopp also acknowledged that Firmino’s work-load is a regular concern to him and his staff.
Asked if he felt the South American front-man was overly fatigued, he said: “Not really but of course it is something we think about 100%. Constantly actually.
“It often leads to the decision that he still has to play. He starts or comes on, sometimes it is better to come in the game later when all the rest are a bit tired but we will see how we handle it.”