From the Times : If the genome of an extinct species can be reconstructed, biologists can work out the exact DNA differences with the genome of its nearest living relative. There are talks on how to modify the DNA in an elephant’s egg so that after each round of changes it would progressively resemble the DNA in a mammoth egg. The final-stage egg could then be brought to term in an elephant mother, and mammoths might once again roam the Siberian steppes.
The same would be technically possible with Neanderthals, whose full genome is expected to be recovered shortly, but there would be several ethical issues in modifying modern human DNA to that of another human species.
Image ripped from here. Reconstructed Neanderthal skeleton, right, and a Homo sapiens skeleton. Some research suggests that it is the human, not the Neanderthal, that strays in the human family tree.