There’s a cluster of Y-chromosomes found in inner Eurasia that vary only slightly, and thus must have a recent common ancestor. They are surprisingly common: there are something like 16 million carriers. The analysts who discovered this (Zerjal et al) concluded the men with these Y-chromosomes are the direct male-line descendants of Genghis Khan, the Master of Thrones and Crowns. They have to be right: no one else conquered such a vast empire and had his sons (and their sons, and so on) rule and enjoy their harems for centuries. More than that, the Golden Family continued to have high social status long after the fall of the dynasties, even into recent times.
Since power descended through the male line, you don’t expect to see the same thing happen with autosomal genes. Genghis accounts for about 25% of Mongolia’s Y-chromosomes, but the general ancestry fraction attributable to him must be a lot lower. Still, what if the average Mongol today is 0.5% Genghis? Upon sequencing lots of typical contemporary Mongols, you would notice certain chromosomal segments showing up again and again: not just in one family but in the whole country, and in other parts of inner Asia as well. If you started keeping track of those segments, you would eventually be able to make a partial reconstruction of Genghis’s genome. It would be incomplete, since any given region of the genome might have missed being transmitted to any of his four legitimate sons (Jochi, Chagatai, Ogedei, and Tolui). They certainly didn’t carry his X-chromosome. You might be able to distinguish the autosomal genes of Genghis and his wife Borte by looking at descendants of his by-blows, if you could find them. Still, even if you managed to retrieve 75% of his genome, that’s not enough to make a clone. It would however, allow sure identification if we found his tomb.
And since he’s likely buried in permafrost, his DNA could be in good shape. Then we could clone him (assuming reasonable continuing progress in genetics) and of course some damn fool would. Will.