Sturridge returned to Liverpool in the summer following an injury-ravaged spell on loan at West Bromwich Albion in the second half of last season, and is now the club's joint-top goal scorer so far this season after Saturday's spectacular equaliser at Chelsea.
Klopp's side will now travel to Italy to take on Napoli in their second Champions League tie of the season, before facing Premier League leaders Manchester City in their final game before the latest global break on Sunday.
"They're one of the best teams around, they reached the Champions League final last year and this year they've started really well, with great organisation".
Ancelotti called the Reds "one of the strongest teams in Europe", before the match in Naples on Wednesday.
"I like Carlo, I respect him a lot", Klopp told reporters.
The Reds opened their 2018-19 Champions League campaign with a thrilling 3-2 home win against Paris Saint-Germain, while Napoli drew away to Red Star Belgrade.
It was a sight that just a few months ago would have been unthinkable - Liverpool a goal down in a big game, and Mohamed Salah hauled off by Jurgen Klopp. "In Germany, we say he's a smart fox", said Klopp.
Alisson also said that he has been an admirer of Jurgen Klopp since his days at Borussia Dortmund and praised the Liverpool boss' management style. Saying all these nice things about me, but it is tactics already.
I don't care too much what people say about us in the moment.
The England worldwide scored a stunning equaliser late on at Stamford Bridge and scored another fine effort during the defeat to Chelsea in the League Cup last week but I still think Firmino will keep his place tomorrow. "He's still here - that would be nice [to meet again]", Klopp added.
But since then it's been better - that was the last time I got a little too excited.
"It was one of the better experiences I've had". He wants to try to bring the very nice fella out of me.
"It was because my behaviour was not so good in the Bundesliga as well".