The Leicester City number one is set to earn his third international cap in Wednesday night's friendly at Wembley.
And Peter, who played in goal for Denmark on 129 occasions, says he is immensely proud of his 27-year-old son.
"It's well deserved, he's played exceptionally well for Leicester over a long, long period of time," he told Sky Sports News.
"He's been very, very patient. Of all the goalkeepers that have been picked in the Danish team over the last couple of years he's been the one consistent player.
"He's played every week and played to a high level and I think it's great that he gets his opportunity. It's in England, it's at Wembley and as a dad I'm really, really proud I have to say."
Kasper was linked with a move away from Leicester during the transfer window in January.
Former Manchester United keeper Peter refused to be drawn on his son's future but admitted playing regularly at the highest level benefits every player's international career.
"The way international football is these days, it's very, very competitive," he said. "I think for anyone playing international football - the higher the level you can play at and consistently play at - the better equipped you are to play these games."
Meanwhile, Kasper says he will be cheering on England at this summer's World Cup following Denmark's failure to qualify for the tournament in Brazil.
"They've got all the players to be a success," he said. "I think sometimes the media and everyone heap a little bit too much criticism on them when it's not quite deserved but I think they've got a great squad and a very good manager.
"Now that Denmark are not going to be there I am going to be hoping that England go far."