His father Peter was a first-choice pick in goal for the national team 129 times, and helped the nation to win the 1992 European Championship, but since he played his last international in 2001 Denmark have struggled to find a replacement.
It took a stunning, one-handed save against Arsenal in the FA Cup in January for Schmeichel junior to finally get noticed by Denmark coach Morten Olsen.
Even though the 24-year-old is in the squad for Saturday's Euro 2012 Group H qualifier against Iceland, he is likely to stay on the bench this time.
In recent years, Stoke City's Thomas Sorensen, Elfsborg's Jesper Christiansen and Stephan Andersen of Brondby have all tried to replace former Manchester United hero Peter Schmeichel, with Sorensen usually getting the nod when fit.
Even if Kasper does make the number one shirt his own in the future, he will have to keep looking over his shoulder as Denmark continue to produce talented goalkeepers.
"We have four very good goalkeepers that have the possibility to go the whole way," Jan Rindom, goalkeeping coach with the Danish FA (DBU), told Reuters in a telephone interview on Friday.
Rindom is a key part of the Danish under-21 set-up where Schmeichel gained 17 caps, and was the driving force behind the development of Denmark's talent programme for young goalkeepers.
CLUB LEVEL
The goalkeeping coach does not believe that Schmeichel junior's relative lack of height, at 1.85 metres, will be a problem in the position.
"If a goalkeeper stops the ball, size makes no difference," he said. "But it also depends on the way the team plays. If you sit back and invite a lot of high balls into the box then it's better to have a tall goalkeeper."
While Peter won five Premier League titles, three FA Cups and a Champions League crown with Manchester United, the younger Schmeichel has had a stop-start career at club level.
He was loaned out on several occasions from Manchester City to gain experience before moving on to Leeds via Notts County.
At Leeds he immediately caught the eye with a number of fine performances but it was his one-handed save from Arsenal's Denilson in an FA Cup third-round tie in January that put the Schmeichel name on the back pages of England's newspapers again.
Even though Olsen is unlikely to give him a game against Iceland in Reykjavik, he has been impressed by Schmeichel and an international senior debut may not be far away.
"He's here to get a taste of the A team," Olsen said of his decision to include Schmeichel in his squad. "We have followed him in England and he deserved his place.
"Kasper is to get a whiff of this and to be motivated to come again," Olsen told reporters this week. (Editing by Clare Fallon; To query or comment on this story email sportsfeedback@thomsonreuters.com)
