Studies say that modern humans didn’t interbreed with Neanderthal becaue N. genes aren’t present in our genetic material. How do they know what a Neanderthal gene looks like? Besides, I’ve seen guys on the subway that look…but I digress.
Note that the analysis so far (AFAIK) has been exclusively on Neanderthal mitochondrial DNA (from outside the cell nucleus). There remains a small possibility that analysis of nuclear genes could show some relationship between Neanderthal and modern populations.
Specifically, if Neanderthal men were mating with modern-type women, the decendents would show no trace of the Neanderthal’s mitochondrial DNA. Whether this was the case, I cannot say.