Rooney was the subject of heavy criticism over the summer after failing to impress for the Three Lions at the World Cup finals.
“I have never thought about quitting,” he told the Sunday Mirror.
“I am 24. Steven is a bit older than me but I think there’s a couple of World Cups left in me yet.
“I’m very proud. For me, to play for England is the pinnacle of my career. In tournaments, we need to do better and I need to do better.
“I’m still young. I’ve still got time to put things right – and hopefully I’ll do that.”
He added: “I want to get as many caps as I can. But the most important thing is to try and get a piece of silverware with England, which would be the biggest achievement of my career if I managed to do so.”