Not true
The problem with slavery is that the people doing the selling didn't have the permission of those being sold. Right now in Nevada you can legally rent a person. Prohibitions against selling organs, against prostitution, against narcotics, and (some arguments[1]) against abortion come down to the idea that no, we really don't "own" our own bodies, in the sense that we're not allowed to do what we want with them.
To borrow Ben's argument from a recent thread, if there were a clear and easy prohibition against the sale of human organs to be found in the constitution, there wouldn't be so much debate about it. Or at least the debate would be completely different.
So no, the sale of human organs has nothing to do, constitutionally speaking, with slavery. And the constitution doesn't seem to have anything clear to say about whether or not we own our own bodies.
[1] There is also the position -- honestly held by many people -- that the fetus is also a whole person deserving of rights. </tangent>
