Liverpool are dominating the Premier League, sitting atop the table having taken 61 points of 63 available.
Klopp's reluctance to tinker with his winning team was evident last summer when the Reds only signed a back-up goalkeeper in Adrian.
So far this month, Liverpool have brought in Japanese midfielder Takumi Minamino from Red Bull Salzburg.
The 25-year-old impressed Klopp so much when the pair faced each other in the Champions League, that the German decided to buy him.
Liverpool haven't faced Bayer Leverkusen this season, but Kai Havertz reputation precedes him.
According to The Guardian, Klopp has discussed the possibility of signing Havertz with the Liverpool board.
The 20-year-old has been heavily linked, as many young German talents are, with a move to Bundesliga giants Bayern Munich.
"They're probably the biggest club in Germany and there are many players that were very successful at a young age that went there," Havertz told Marca.
"Therefore, I get linked with Bayern, but we'll see what happens.
"There are players that want to stay close to their family and others say, 'I want to live in another country'. There's something clear: if you want to be a star in Germany, you can't go wrong with Bayern."
If Liverpool were to do a deal for Havertz the mooted fee is around £100m - meaning they would have to smash their transfer record.
The good news for reigning Champions League winners is that they are currently one of the most attractive destinations in football.
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