Klopp has been telling Danish publication Ekstra Bladet of his admiration for Dolberg.
"Who doesn't know Kasper Dolberg? You can't play at Ajax without being noticed," he said. "Kasper Dolberg has a very great future. He is a fantastic player.
"I love Danish players. I had Leon Andreasen at Mainz, he was a monster. I also have fond memories of Bo Svensson. And Mohamed Zidan - he is probably half Danish, because his wife is Danish!
"But it's not that they are Danes, it is all about their qualities."
"We were very interested in [Christian] Eriksen, but we had to choose between him [Henrikh] Mkhitaryan and [Kevin] De Bruyne," he said. "Eriksen is a great player. Everyone would love to have him on their team.
"At that time we had three players, we went after - Henrikh Mkhitariyan, Kevin De Bruyne and Christian Eriksen. We scouted all three very intensely, but we knew we could only get one. We were happy to get Mkhitaryan.
"Since then, Christian Eriksen has taken a great step at Tottenham. He's very strong."
But the Liverpool boss ruled out a move for the Spurs midfielder, saying: "'No, we would not act in that way towards Tottenham."