The Reds only need two more victories to wrap up a first top-flight title in 30 years, but Klopp is eager to do much more than the bare minimum.
Liverpool have 27 points left to play for and the German wants to take them all, which would mean a total of 107 – exceeding Manchester City's all-time best tally of 100 from the 2017-18 campaign.
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With fixtures set to resume on June 17 following a lengthy coronavirus-enforced shutdown, Liverpool are tantalisingly close to glory, but Klopp knows there is work to be done.
"It's nice to think about it but we are not champions yet and we know that," he told BBC Sport.
"We know we are close but close is not there. There are 27 points left for us and we will try everything to take them all.
"We are still not champions. We have to play football games and we have to win them.
"We don't want to stop winning after two games or whatever it is. I don't see results written in the stars; we have to work really hard."
Klopp's side lead the way by 25 points but hit patchy form before fixtures were halted, losing their unbeaten league record to Watford, suffering defeat to Chelsea in the FA Cup, and seeing their Champions League defence ended by Atletico Madrid.