Paeleoanthropologist Don Johnson thinks not:
The reason? Johnson believes we were too picky about our mates: "I don’t think we interbred with the Neanderthals at all. There are some people who think that there was some level of interbreeding. I think that we look so biologically different that we looked and we acted so different and we culturally were so different that we would not have had interbreeding between two species."