The Coca-Cola Championship side have had two offers rejected and manager Owen Coyle has ruled out a fresh bid for the 20-year-old winger.
Driver came through the youth ranks at Hearts and is now a first-team regular after making his senior debut in August 2006.
He has refused to rule out a move south of the border one day but insists he is committed to the Tynecastle club for now.
"The speculation about Burnley hasn't affected me," he said.
"I haven't heard anything from the club or anyone else so I just need to get my head down and keep working hard and get on with it.
"I'm still only 20, have loads of improving to do, and I'm looking forward to getting back playing again after missing the last bit of last season through injury.
"I am a Hearts player and I want to concentrate on getting fit for the new season.
"I want to do the best I can in my career and I want to improve as much as I can. If I can do that, then maybe the chance will come to play in England.
"Obviously it is a boost that someone is interested and shows I am maybe doing something right but I just want to keep improving as a footballer."