Well, maybe not quite yet. But work is underway.
In Austria, researchers took both embryonic stem cells (i.e. from human embryos) and adult skin cells, then did some "lab magic" and in about a month the cells grew and self-orgaized into what the researchers termed "brain-like organoids" 3-4mm in size that showed "neural activity".
Think of it! A few flakes of skin can become the startings of a human brain. Now that's not to say that these litle bits had consciousness, that's many more steps ahead.
They have survived a year (as of when the article went to publication in the journal Nature,) but have not grown any larger, apparently because at this point there is no blood supply in. (But other research in other labs is focusing on generating bio-artificial blood vessels.)
What about the ethical issues of growing even a tiny human brain? The researchers are aware of the issue, and the Austrian team does not want to see larger human brain specimens grown now, as that would be "undesirable."
Gary Marcus, in a New Yorker article, looks at this same research, though taking a much longer look at the implications of where this kind of work may lead decades or a half-century from now.
"But we’ll also need to confront immense ethical quandaries. What rights does synthetic brain tissue have? Should a 3-D-printed brain have the right to vote? To an education? To terminate its own life? (Or to not be terminated?) For now, these questions are still just another round of thought experiments. But it’s more likely than ever that such thoughts might some day be held by just another brain in a jar."
Beyond all that, there's still one other big issue: even if we can "grow" a complete human brain, where is the mind? That is the biggie we tackle in my technothriller, A REMEDY FOR DEATH --Playing God with Body, Soul, and Biotech, . . . though suggesting an approach other than bio-science.