Interestingly enough, the rumor claims that we will be looking at both the Galaxy S7 Edge and the Edge Plus. This seems to suggest that Samsung will be doing away with a flat screen version of the phone completely, a dangerous but bold choice. However it would make sense as there have been reports earlier this year that the Galaxy S6 Edge actually sold just as well, if not better than its flat screen sibling.
For those unfamiliar, the Edge Plus will basically be the larger model of the two. Samsung sort of did that this year with the launch of the Galaxy S6 Edge earlier in 2015, but it was only a couple of months ago that they launched the larger Galaxy S6 Edge Plus. With this report, it looks like both variants could be launched at the same time.
As to when the phones will be launched, the latest rumors have suggested that we could be looking at the 19th of January. This puts it after CES 2016 and a couple of weeks before MWC 2016, but until we get the actual invites, take it all with a grain of salt for now.