At the very end of the press release for the John Wick virtual reality game, it says the following:
Lionsgate is currently developing John Wick 2 for release next September.
Note: Since the press release was generated by Starbreeze Studios and they are collaborating with Liongate, I would assume that the info on JW2 is accurate. If they are looking for a release date in September 2016, then it would appear likely that the film would start shooting sooner rather than later considering September 2016 is just a hair over a year away. The weapons and aerial training and making nice with Jumpy the stunt dog also suggests that a JW2 shoot is in the near future.