Did Neanderthals Possess the imago dei?

I just read a fascinating piece about the relationship between early humans and Neanderthals at the Big Ideas blog. Realizing that early humans and Neanderthals "coexisted" and even interbred, made me wonder if we should consider them to also have the imago dei? This of course strays into a couple of different and tenuous areas of inquiry. One has to do with the fact that any interaction between the two groups would necessarily have to have occurred more than 20,000 years ago, when Neanderthals went extinct. That immediately pushes back at any literal reading of the creation narrative, which among young earth creationists, typically sees the earth as being less than 10,000 years old. It also raises the very basic but also notoriously difficult question of what does it even mean to possess the imago dei or the image of God? So if our ancient DNA was complementary enough so that we could interbreed with our Neanderthal cousins, a DNA difference that would need to be less than 3% for successful breeding to occur, can we legitimately say that we homo sapiens  have the imago dei, but the Neanderthals didn't?