The Scot has come tantalisingly close to a breakthrough, reaching three previous Wimbledon semi-finals, two Australian Open finals and one US Open final, but has always come up short in the final shake-up.
James won his first NBA championship with the Miami Heat last season after a few close shaves and Murray, a big basketball fan, said it was inspiring to see.
"LeBron James would be a good example," said Murray when asked if he could compare his situation to other sportsmen.
"He obviously is a great basketball player. He came very close to winning quite a lot of times.
"Him winning this year I'm sure was massive. For me as a basketball fan it was nice to see.
"I would say for me I guess it's a similar situation. I've been close a lot of times and not quite made it.
"You know, you just have to keep putting myself in the position, and hopefully it will click."
Murray, who came through a fierce battle with Spain's David Ferrer in the Wimbledon quarter-finals, has been criticised for failing to perform in three grand slam finals, albeit losses to all-time great Roger Federer twice and world number one Novak Djokovic.
Often low-key and dour when talking about his tennis matches, Murray warmed to the task when discussing James.
"I follow basketball a lot and watch a lot of the sports news and stuff," he said. "There's a lot of people out there that didn't want him to win.
"There's a lot of people that said he would never win. There's a lot of people who said he never played his best in finals. In the fourth quarter of games he never steps up.
"Then you see how he played the whole of the finals, the whole of the playoffs.
"Sometimes it takes guys a bit longer than others."
Murray will hope James's exploits are an omen as he prepares to do battle with Jo-Wilfried Tsonga on Friday when victory would make him the first Briton to reach the Wimbledon men's