It is a step up for Cork after similar spells with Bournemouth, Scunthorpe, Southampton, Watford and, most recently, Coventry.
Dad Alan, who helped Wimbledon's 'Crazy Gang' lift the 1988 FA Cup, will be taking a keen interest.
Cork, who was born a year after that famous win against Liverpool, said: "I can take a lot from him as he tried to help out and tried to help me improve.
"He had a really good career and played his fair share of games. Mind you he was a different type of player to me.
"He was the kind who would shout 'Get into the box and head it son'. He was part of the Crazy Gang and all that stuff. All I remember was the long beard and the bald head!"
Cork is pleased with his progress this season at club and international level, where he is coached by former England full-back Stuart Pearce.
He said: "I had a good spell at Coventry and played regularly for four or five months. They wanted me to go back but nothing came of it and I am happy now to be at Burnley.
"I have also learned a lot from the Under-21s with someone like Stuart Pearce being in charge.
"There are some good, exciting players from the Premier League in the squad and it is great to be involved."