Danish legend had agreed to become a Red before joining Juve...
The attacker went on to star for Juventus, Barcelona and Real Madrid, but things could have worked out very differently.
"Yes, in 1983 I had the opportunity to sign for Liverpool," Laudrup told the Reds' official website.
"We actually agreed a deal and I came over with my father to talk to Liverpool's representatives. We agreed a three-year contract and went away thinking it was all done.
"But two weeks later they came back saying they wanted to offer me the same package, but for four years because I was still young and needed time to develop. I was disappointed because although nothing had been signed, we had an agreement.
"I decided not to join them and people thought I was crazy. This 19-year-old was turning down the great Liverpool. It wasn't really like that though. I just felt an agreement is an agreement and people should stick to what they decide. After that, I had other offers and went on to join Juventus. That's football for you."
One current Anfield star Laudrup rates is England midfielder Steven Gerrard. The Dane thinks the Reds' skipper is right up there with the best players in the world.
"Of course. He has been the symbol of Liverpool for many years now," Laudrup added.
"I don't think people can imagine a Liverpool team without Gerrard. It is like Raul at Real Madrid and Puyol at Barcelona.
"They are a rare breed, these types of players. He had the possibility to leave and couldn't - the club is in his blood."
Another current Reds star who impresses Laudrup is Fernando Torres, though the Dane is uncertain whether the Spaniard is currently the world's best striker.
"Well he's right up there. I think there are a lot of great strikers in Europe," he explained.
"In the Premier League you have Wayne Rooney and Didier Drogba as well. Then you have the likes of David Villa, Zlatan Ibrahimovic and Samuel Eto'o.
"I don't know if you can identify one player as the best but he's definitely in that bracket with those guys. He's had some injuries recently but when he's on form he can be unplayable.
"Hopefully he will return soon and hit form for you at just the right time. He would then be ready for the World Cup too, which is the biggest stage of all."