The youngster wrote to the German for an assignment at Glenswilly National School in County Donegal, Ireland.
He implored Klopp to "please make them lose" and added: "I hope I have convinced you to not win the league or any other match ever again."
Despite Daragh's dismay at Liverpool's winning streak, Klopp replied to his letter:
The 52-year-old explained he could not grant the request, but he also offered the schoolboy some hope:
"As much as you want Liverpool to lose, it is my job to do everything that I can to help Liverpool to win as there are millions of people around the world who want that to happen, so I really do not want to let them down.
"Luckily for you, we have lost games in the past, and we will lose games in the future because that is football."
The former Borussia Dortmund boss also said United are "lucky to have" him and his passion for football and the club, and he spoke about the respect the two rivals have for one another.
Daragh spoke about the letter he received with Adrian Chiles on BBC Radio 5 Live:
BBC Radio 5 Live @bbc5live
🗣️"I didn't expect to get a reply from Jürgen Klopp at all" 10-year-old Daragh Curley tells Adrian Chiles his shock at the @LFC manager's personal reply to his letter asking him lose⚽️ Eddie Jones best watch out as he's Daragh's next target 📲Read more https://t.co/Ec7ELTc9Tv https://t.co/o21UwmF5Mf
Daragh's father, Gordon Curley, told BBC News NI:
"My wife Tricia was up in the local post office/shop, and she was told that there was a registered letter there for Daragh Curley.
"She was wondering who would be sending Daragh a registered letter, but when she mentioned it to Daragh he said 'oh it's Jurgen Klopp.'
"And it actually was Jurgen Klopp."
He also said Klopp is "a decent, decent guy," and praised him for writing about "sportsmanship and respect" in the letter.
As for Daragh's hope of the Reds losing, it doesn't look set to happen in the Premier League any time soon, but they did suffer a 1-0 defeat to Atletico Madrid in the UEFA Champions League on Tuesday.
Opta's Duncan Alexander noted the contrast between their domestic and European form, despite the Reds having won the Champions League last season:
Liverpool still have the second leg of their last-16 tie with Atletico to play, so they're not out of the running in that competition yet.
In the Premier League, Liverpool last suffered defeat on January 3 last year, which was their only loss in the league in the 2018-19 season.
They're unbeaten in this campaign, having picked up 25 wins from 26 matches.
As a result, they're 22 points clear of closest rivals Manchester City with 12 games remaining.
Liverpool are so far ahead, they can still win the league even if their form drops significantly during the run-in:
What's more, Klopp's men will only need 15 points to guarantee the title if City win all of their remaining games.
The Citizens have failed to win nine league matches so far—six of them defeats—and they're yet to pick up more than three consecutive victories, so in reality Liverpool will likely need fewer points.
Liverpool also remain in the FA Cup, in which they'll face Chelsea at Stamford Bridge in the fifth round.