Rodgers left the Swans to join Liverpool during the summer and made the 22-year-old midfielder one of his first acquisitions as Reds boss prior to Laudrup's arrival. The pair is now set to come up against the South Wales side for the first time since the move, but the Dane insists his mind is focused solely on the Capital One Cup clash.
"For me this is nothing different, I want to win all the games," Laudrup told BBC Sport. "I know there is something special when you see former players and coaches, but for me it is Swansea against Liverpool, not against Brendan Rodgers or Joe Allen."
The Swans have never progressed further than the fourth round of the League Cup, and will be hoping to achieve the feat for the first time in the 100-year history of the club.
"It's at Anfield and it is a big game in a competition where if we win we can claim a place in the record books of Swansea City," Laudrup continued. "I want to win every game we play, not only the ones where we are against ex-managers. There was one of those 10 days ago [against Roberto Martinez's Wigan] and we won that."
The visitors will be without influential goalkeeper Michel Vorm for the next eight weeks after the Dutchman suffered a groin injury, meaning Gerhard Tremmel is set to deputize in his place.
"It's a huge opportunity for Gerhard," Laudrup added. "Obviously we're very sad for Michel, but it's a part of football. We all know that the position of goalkeeper is very special - you play all of the time or you play very seldom. It's much different to being an [outfield] player."