The 26-year-old became the first British man to win a Grand Slam since 1936 last year when he clinched the US Open and in the same year he was also a finalist at Wimbledon but was defeated by Roger Federer.
The Sun quotes Murray as saying: "I've thought about finishing my career not winning Wimbledon and I'm comfortable with that. I'm going to win Wimbledon. To make that my No 1 priority would be counter-productive.
"I'm doing all I can to give myself the best possible chance. I work as hard as I can and as long as I give 110 per cent on the court that's the best that I can do.
"When I've started to accept those sort of things I've started to play better tennis."
Murray will face Benjamin Becker in the first round at Wimbledon later today.