Nail, head.
Don't get me wrong I like Klippity but he could build a Dortmund team whilst at the same time offering thereabouts guaranteed CL football. Plus Germany have and still are going through a purple patch of producing national talent which don't particularly want to leave in search of riches abroad and they were the second best club in Germany.
All of that helps hugely in building a squad and Liverpool currently cannot offer any of what Dortmund did. Great youth? Nope (perhaps bar Ibe) guaranteed CL football, certainly not, one of the best teams and payers so can keep top talent? Nope.
He first managed Mainz who finished 14th the year before he took over in the second division, he immediately made them compete for promotion and achieved it in his third year and qualified for Uefa cup in the second year in the top division, did get relegated but this was a small club with little money. He still achieved a great deal.
Dortmund between 03/04 and Klopp taking over didn't finish above 6th, were 14th the season before he took over, a strong club 00-03 with a win and top three finishes they had 5 years being not great. THey most certainly weren't a strong CL side helping him build a squad. He finished 6th, then 5th, then won it two years in a row, second twice in a row and one 7th with literally 6-7 months of the season in a terrible injury crisis and great form when the injuries went away.
At both clubs he built the squads up himself and achieved success off his own back, not being some top 3 CL club with more money than anyone else.
http://www.transfermarkt.com/borussia-dortmund/alletransfers/verein/16
They became a top 2 club with consistent CL appearances while spending 2-3mil net a year and less than 15mil a year on players going from 14th to 1st in the league.
This is precisely what Liverpool need, someone spotting talent, someone nurturing talent, someone who is a brilliant coach, will get the best out of the team, plays a smart game that will do excellently in europe and someone unafraid to use youth players.
He's one of the best managers in europe precisely because he is one of the few not to take over big CL teams, have massive budgets and couldn't buy just whoever he wanted. Ancelotti, Mourinho, these are guys who take over strong teams and can buy who they want. Klopp had to build a team with little and turn it into a great side and he did that better than pretty much anyone else has in recent history... well, Simeone took over a team not close to consistently in CL or the top 4 and made them incredibly competitive however Atletico have spent huge while selling a few players for huge fees.