Klopp succeeded Brendan Rodgers in the Anfield hot seat, although at the time there was speculation over Ancelotti possibly taking charge. The Italian had left Real Madrid at the end of the previous season.
Ancelotti is now in charge of Liverpool's Merseyside rivals Everton, and the two teams will square off on Sunday in the third round of the FA Cup. Ahead of the contest, the Toffees coach confirmed he had a conversation with the Anfield club, although he said it's clear they made a smart choice in Klopp, per Chris Bascombe of the Daily Telegraph.
"It was after (I left) Real Madrid, I had a chat with the owner," he said. "They were looking for a new manager, but I think they made a right choice with Jurgen. He is doing fantastic work at Liverpool, so well done."
It's difficult to argue with Ancelotti's assessment, as Klopp has transformed the fortunes of the Reds during his time in charge.
Last year, the team won the UEFA Champions League title, and at the moment, they are 13 points clear at the top of the Premier League table.
Per B/R Football, Thursday's 2-0 win over Sheffield United means they went undefeated for a year in English football's top flight:
Ancelotti is the only coach to have masterminded a win over Liverpool in the Premier League or Champions League this season, as his Napoli team were 2-0 winners in the latter.
On Sunday, he will be hoping to repeat the trick when his side visit Anfield. It will be a huge test, though, as Everton have a rotten record at their former stadium, with no wins there since 1999.
Ahead of the match, Ancelotti appeared to be keen to embrace the local rivalry in his press conference:
The Italian brings incredible experience to Goodison Park, having won three Champions League titles and numerous other honours. His influence will no doubt be key if Everton are to spring a shock.
Klopp was full of praise for his opposite number in his pre-match press conference, too, saying he thinks he'll fare well with the Toffees:
For Ancelotti, a win over Liverpool would be a fantastic way to quickly earn favour with fans of his new club. With the team languishing in mid-table in the Premier League, a cup run in 2020 would keep focus and spirits high on the blue half of Merseyside.
With the Premier League and Champions League taking priority for Liverpool this term, Klopp will likely make a number of changes for Sunday's match, potentially giving Everton the chance to finally break their Anfield hoodoo.