Much of the focus ahead of the Capital One Cup last-16 tie has been on Liverpool boss Rodgers facing his former charges for the first time since leaving the Liberty Stadium.
Despite guiding the Swans to the promised land of the Premier League, and leading them to an excellent 11th place finish, the Northern Irishman, who also prised midfielder Joe Allen away from south Wales, can expect a hostile reception from the travelling support.
Laudrup knows a thing or two about having to face the rancour of opposition fans after leaving Barcelona for arch-rivals Real Madrid in 1994, and his first return to the Nou Camp has stuck in the Dane's memory.
Laudrup does not expect Rodgers to receive anything like that level of antipathy, and believes time will ultimately heal the hurt felt by those angered by his decision to leave Swansea.
"I don't know how much stick Brendan will take on Wednesday, but I can tell you it won't be as much as I did when, after five years playing for Barcelona, I went back there with Real Madrid," he said.
"You could say the fans weren't that happy to see me - there were 100,000 whistling at me every time I touched the ball.
"The noise was incredible. It wasn't very pleasant.
"But years on, I can now go to the Nou Camp and be welcomed there. As I said, time is a great healer.
"Football is about feelings, sometimes very strong feelings. From the highest love to the deepest hate.
"That's how it can change, very quickly. You cannot alter it. That's why supporters react the way they do.
"But over time, you begin to appreciate what a particular person did.
"That's why I believe that eventually they will realise what progress Brendan made here. He did a great job for the club."
Wednesday will mark Laudrup's first visit to Anfield as a player or a manager, having missed the chance to play at the famous old ground due to the ban placed on English clubs playing in Europe following the Heysel disaster.
And he admits the Reds were a team he admired in his youth, and is eagerly awaiting the chance to experience the matchday atmosphere on Merseyside.
"They were my team as a kid. I watched them as a kid, I watched them on television back home in Denmark," he said.
"I loved the team, the atmosphere. But I never got the chance to play there, because Liverpool were banned from Europe for a long time after Heysel.
"I've only been there once, with Spanish television when they played Barcelona a few years ago.
"Now I'm looking forward to being involved there - even on the touchline."