The Reds secured their first championship for 30 years last week, which led to fans gathering in the city and outside Anfield.
The celebrations have been criticised amid the coronavirus crisis and Klopp has urged supporters to behave responsibly.
In an open letter to fans in the Liverpool Echo newspaper, the 53-year-old manager said: "I am a human being and your passion is also my passion, but right now the most important thing is that we do not have these kind of public gatherings.
"We owe it to the most vulnerable in our community, to the health workers who have given so much and whom we have applauded, and to the police and local authorities who help us as a club not to do this.
"Please - celebrate - but celebrate in a safe way and in private settings, whereby we do not risk spreading this awful disease further in our community."
The former Borussia Dortmund boss has urged Liverpool supports to not waste the efforts that have gone into fighting Covid-19.
He wrote: "If things were different I would love nothing more than to celebrate together, to have a parade that would be even bigger than the one after we won the Champions League last year, so that we could all share this special moment, but it just is not possible.
"We have all done so much to fight Covid-19 and this effort cannot go to waste.
"When the time is right we will celebrate. But for now, please stay at home as much as possible."