According to Dominic King of the Daily Mail, Liverpool's owners, Fenway Sports Group, are eager to get the German signed to new terms, but Klopp has stalled over extending his contract.
He has now made it clear that he is not intending to jump ship and will see out his current contract at the very least, per King:
"I cannot imagine a day [when I will not be Liverpool manager], but it is not important. I don't want ever to be in a situation where people are annoyed that I am still here. That's the truth. You have that situation in football. It must always be a win-win situation.
"At this moment, it is 100 per cent, and we will see how long that will be. Whatever discussions came up... a few headlines that I saw, not a lot, that I will finish for sure in three years, that I will sign a contract and all that stuff. I have three years. It is all good. I love this team—they are brilliant.
"The age group of the boys is good; my age is good for what I have to do. The owners like what I do; I like what the owners are doing. I will not leave before the contract is ending. That is my side. We have enough time to make decisions in that department. There is no need to do it now."
Klopp, 52, was appointed Liverpool manager in October 2015 as Brendan Rodgers' successor.
He could only lead them to eighth in the Premier League in his first season in charge. But he has since overseen a remarkable improvement in the Merseyside giants.
Consecutive fourth-placed finishes in the English top flight were followed last term by a runners-up spot to Manchester City, when Liverpool lost just one game all season and accumulated an astonishing 97 points:
The Reds also won the UEFA Champions League in 2018-19, beating Tottenham Hotspur 2-0 in Madrid in the final back in June.
A string of astute purchases and Klopp's tactical acumen have combined to make Liverpool one of Europe's best sides once again.
It is no surprise, then, that Liverpool's owners and fans are keen to ensure the former Borussia Dortmund boss stays at Anfield for as long as possible.
He has taken them closer than ever to ending their league title drought, which stretches back to 1990.
And in 2019-20, Liverpool will likely again be the only side capable of challenging Pep Guardiola's City for the title.
The Reds kick off the new campaign on Friday, August 9, with a home fixture against newly-promoted Norwich City.