Rodgers moved from the Liberty Stadium to Anfield over the summer and current Swans boss Laudrup thinks that Rodgers' treatment by the fans in Wednesday's League Cup clash will pale in comparison to his time in Spain.
"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," said Laudrup.
"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."
However, the former Getafe coach says that Swans fans will forgive Rodgers for moving to Liverpool over time.
"But years on, I can now go to the Nou Camp and be welcomed there," he added. "As I said, time is a great healer. That's why I believe that eventually they will realise what progress Brendan made here. He did a great job for the club."
Liverpool are the current holders of the League Cup, having beaten Cardiff City on penalties in last season's final in February.