The guy who is widely reported to be looking for a mother for a cloned Neanderthal baby is doing nothing of the kind. George Church, a Harvard geneticist, was quoted accurately in the magazine Der Spiegel when he speculated about whether such a thing could be done. But this led immediately to global headlines saying he was going to do it and was looking for a suitably adventurous woman to carry the baby.
There was a thread on the National Association of Science Writers group I belong to complaining scientists talk less to the media than they used to. Well, this episode illustrates why.
This item on LiveScience explains how hard this would actually be, and how unlikely it is with near-term technology. Because we have sequenced Neanderthal DNA doesn't mean we can jump from that to a clone. We can't, at present. And a really troubling point is that, even if we could, we'd have dozens of failures for every success. There's no ethical way to think about that.
Of course, if someone really WERE looking for a surrogate mother, in this age of people doing anything to be on reality TV, someone would do it. And it would be televised.
Finally, Isaac Asimov wrote a very touching story, The Ugly Little Boy, about a woman asked to be caretaker for a Neanderthal boy, albeit one brought back through a time-sampling device. It was later expanded into a collaborative novel.