A LinkedIn CV claims costume design work took place in November 2012
Whilst this may seem like a bit of a long shot, it seems like Resident Evil 7 may have begun development last year shortly after Resident Evil 6 shipped. A LinkedIn profile has suggested as least some pre-production design has been done between November 2012 and January 2013.
Karen Brakenridge had on her CV a role of Costume Designer for "the video game Resident Evil 7" on her profile whilst working at House of Moves, a well known Mo-cap studio. The job listing isn't on her profile anymore but an eagle-eyed NeoGAF user noted the details. At first I thought "Well, maybe this could just be the next Resident Evil movie?" but they're only up to the fifth film so far in the franchise.
It seems obvious that there will be another main installment in Capcom's zombie franchise, despite Resident Evil 6's failure to meet the publisher's target. Capcom are going to keep pumping out Resident Evil games as long as people keep buying them and the chance of Resident Evil 7 existing in some way isn't a surprise. What we don't know is what form the game will take after the different styles of RE6, Revelations and Operation Raccoon City.