Cork, 32, has not scored in over three years and would love to end his barren run in the home game against Everton on Boxing Day.
“A goal would be nice, I’m due one. It’s been a long time,” Cork said.
“My son’s just getting to an age where he keeps getting on at me to score some goals, so I need to get one for him really.
“I’ve got a celebration planned for him. He’ll never see it probably!
“I play in the garden with him. We always do skills and mess about and he said: ‘Daddy why don’t you ever do skills on the pitch, you can do them in the garden?’
“He’s told me I need to do this celebration and do that. He’s just had a year where he’s got mad into football. I think it was the Euros that really got him excited for it.”
Cork is in his fifth season with Burnley and scored the last of his three Premier League goals in 128 appearances for the club in a 3-1 home defeat to Liverpool in December 2018.
The Clarets are anxious their clash with Everton goes ahead after their two previous scheduled fixtures – against Watford and Aston Villa – were postponed due to coronavirus.
“We’ve got a bit of catching up to do now,” Cork said. “We’ve got three games (in hand) on a few other teams now, three games on Leeds (and Newcastle).
“But even though we haven’t played the table doesn’t look too bad. We’ve got some games to play and it will give us a good chance to catch up.”
Burnley have maintained their top-flight status throughout Cork’s second spell at Turf Moor. He was signed for a reported £10million from Swansea in 2017, having had two previous loan spells at the club.
The Clarets are currently third from bottom, two points from safety, but are seasoned campaigners at getting themselves out of trouble.
They also have a game in hand on the team immediately above them, Watford.
“I feel like we’ve got the players, and the team has shown in previous years, that the second half of the season suits us,” Cork added.
“Sometimes at the start of the season we struggle, but have a determination to dig in over the colder months when the fixtures get a bit busier.
“We’ve got the sort of attitude that we want to get stuck in. We want to stay up, we want to fight for it and that’s served us well over the last few years.”