The Ghana midfielder has less than 12 months left on his current deal at Tynecastle and has long been tipped for a move to the Premier League.
However, the 28-year-old claims he is settled in the Scottish capital and would be happy to stay.
"I have not spoken to the club about an extension but I am happy here," he said.
"My family, my kids are happy so if Hearts come to me and say they want to talk about extending my contract, then why not?"
Kingston missed a big chunk of last season through injury and he hopes things will improve this term.
"I am feeling good and hoping that no more injuries come my way," he said.
"I want to give more for the club. I have missed a lot of important games but I am hoping that this season everything will be fine."