Praise be to Allah.
It is permissible to transplant a kidney for one who needs that, if a kidney is available in a permissible manner. But it is not permissible for anyone to sell his kidney or any part of his body, because there is a warning regarding the one who sells a free man [as a slave] and consumes the price, and selling body parts comes under that heading, because the human does not have ownership over his own body. That warning also serves to bar a means that may lead to trading in body parts – this is what appears to me to be the ruling in this case. It also serves to avoid abuse of weak people and stealing their kidneys in return for money.
Al-Muntaqa min Fataawa ash-Shaykh Saalih al-Fawzaan (3/62).