Probably by Tuesday, when they usually post Crown Store news. Not posting it til the month actually starts isn't unprecedented. A lot of the December items push into early January probably for this reason, so we're set for a while. Hopefully the staff had some time off at the end of the year, if you can bear to wait a few more days
One way to tell is to go to Crown Store in the game, select Featured, and see how many days are remaining on the Limited Time Offers. This isn't a guaranteed method, because there might be different offers that have different numbers of days remaining. For instance, right now some offers have 2 days remaining, while others have 4 days remaining. But it should give you a pretty good idea.