The power forward had been expected to miss the remainder of the playoffs after picking up a calf strain against the Los Angeles Clippers earlier this month.
However, Thunder general manager Sam Presti told reporters: "We're surprised that we're here, although grateful that he's made enough progress to say he's not ruled out.
"I think it's important, when you look at this, to recognise that we're not saying that he's playing, but what we're really trying to indicate is that the information is telling us that we can't rule him out.
"A big part of this is the swelling in his calf has reduced incredibly rapidly, more so than any of us could've expected or our medical staff could've projected. And as a result of that he's demonstrating a function level and a stability level that's better than where we thought we would be."
The Thunder currently trail the series against the San Antonio Spurs 2-0.