The 40-year-old has also guided the Whites to the top of the League One table but Grayson, whose managerial career started at Blackpool, has dismissed speculation linking him with a move back to Lancashire.
Burnley are looking for a new boss after Owen Coyle left for Bolton Wanderers.
"I have only been here a year and it took a lot for me to leave Blackpool. I had a good job there," Grayson told the Yorkshire Post.
"This was a fantastic opportunity and I have said all along that someone will take this club back into the top flight. Hopefully, that will be me.
"I am fully focused on achieving my target of getting this club promoted into the Championship and beyond.
"People can speculate with Burnley or whatever club they want but I am committed to trying to take this club forward.
"I am flattered because everyone wants to manage in the Premier League. But my ideal scenario is to manage this football club in the Premier League."