Barnes has made 30 appearances so far this season, netting six times and providing three assists for Sean Dyche's side in the Premier League.
Heaton and defender Michael Keane are just two of the Burnley stars being linked with moves away from the club but the 31-year-old, who has two years left on his existing contract, says he is happy to stay.
"It is about playing Premier League football and continuing to work at the worldwide set-up", he said.
"But more than happy with where I am at the moment".
Sean Dyche has targeted strengthening his squad ahead of next season's Premier League campaign amid continued speculation regarding the future of the Clarets' big names.
"It's always a good stimulus when they see players coming in and they have to fight for their own shirt, so we've got to add more".
Burnley, who had been fighting relegation for much of the season, could finish as high as 11th if they beat West Ham United in their final match on Sunday and other results go their way. "Whatever happens we will deal with it and we'll keep moving forward".
Instead Dyche is focused on challenging his players to finish the season on a high with a victory against the Hammers at Turf Moor.
As they prepare for life back in the Premier League, the Magpies are trying to improve in all areas of the pitch and have apparently identified the Clarets attacker as an option to add firepower.
"We're not finished there - there's still places to play for".