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Cody Gakpo, who left PSV Eindhoven for Liverpool earlier this month, led the line for Klopp's side in the FA Cup against Wolves on Tuesday night and had to take on a more prominent role following Nunez's absence.
When asked if Nunez is ready for the visit of Chelsea, the Reds boss simply replied: "Yes".
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There is expected to be several changes from the side that featured at Molineux.
"I never had one headache with selection, it's now 1.45pm, training at 4pm, we have meetings and I get all my information then," Klopp said on his team selection.
"So let me see if I get a headache or I get some information which will give me another headache.
"I'm completely fine, I hope they are all fit and ready. We will find a good team."
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Liverpool's talented teenager Stefan Bajcetic could be one in contention to start in the Reds midfielder.
"He was injured for two games, he is my thoughts [for selection]. It doesn't look like we have to be careful [around his development]," replied the German.
It has been 70 years since the Reds last suffered three successive losses in their opening three league games of a calendar year, as they lost to Stoke City, Manchester City and Portsmouth in January 1953.
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Klopp will be hopeful of avoiding the same fate, as he takes charge of his 1000th game as a manager.
He has been inducted into the League Managers Association's 1000 club, with a tribute from Sir Alex Ferguson.
The German reflected on his career, claiming it was almost over before it started when Mainz nearly suffered relegation to the third division in Germany.
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Since then, Klopp has gone on to win two Bundesliga titles, the Premier League, the Champions League, the Club World Cup, the FA Cup and the League Cup in his 22 years in the dugout.
"Crazy, I never though about these kind of numbers and never thought I'd be allowed to do it for that long. You have to work 22 years and somehow arrive there.
"I am really blessed. Three fantastic clubs gave me an opportunity to do my job. When you come in somewhere you never know how it will go and I'm really lucky about how things have happened, 1,000 is a crazy number.
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"I've done the job I love for the clubs I love. I'm really blessed with it. I am still enjoying it, absolutely. Maybe people should get an honour for 1,000 good games, but I'm not sure anyone would get old enough to do that!"
talkSPORT will have live coverage of the game between Liverpool vs Chelsea at Anfield, with kick-off at 12:30pm.
To tune in to talkSPORT's live commentary through the website, click HERE for the live stream.