The Heat trail the San Antonio Spurs 3-1 in the finals, knowing that no team has ever won the last four games of the series to win the title in the history of the competition.
"It would be in the range of, `Why not us?'" James told reporters. "Why not us? History is broken all the time. And obviously we know we're against the greatest of odds.
"History is made to be broken, and why not me be a part of it? That would be great. That would be a great story line, right?
"But we'll see what happens. I've got to live in the moment, though, before we even get to that point."
The Heat face off against the Spurs in game five of the series later today.