The 31-year-old has played a pivotal role in the Clarets' relatively carefree season, keeping 10 clean sheets in his 34 appearances.
Despite links to Newcastle United and Crystal Palace in recent weeks, Heaton is "more than happy" at Turf Moor after receiving recognition at international level with England, and now wants to add more caps in the coming years.
"It is about playing Premier League football and continuing to work at the international setup," FourFourTwo quotes him as saying.
"I'm delighted to be involved in that and have a taste for it - and now I've got a hunger for more. I want to continue improving every day and I'm more than happy where I am at the moment."
Heaton agreed fresh terms at Burnley in July 2016 to keep him under contract until 2020.