Pure speculation but there are a couple of things lining up that could lead that way. 23rd July is Comic Con which is essentially feels like one of the last big hoorahs of this era (you wouldn't want to go 'Hey here's your new Doctor!....but now here's a panel featuring the old guy). Capaldi was announced on 4th Aug 2013. Filming for the Christmas Special has just ended and, if they haven't already, they're probably going to do the 13th Doctor's regeneration soon enough.
So I'm going for either the last weekend of July or the beginning of August. That way you're far enough out of the way of Series 10 not to seem rude, early enough that it doesn't leak, and, depending on the choice, early enough to begin building anticipation before filming starts.
I'd almost guarantee it.
As much as I'm curious to see who they end up picking for the Doctor, I'm also excited for all the ancillary changes like new TARDIS interior, new logo, new theme, new title sequence etc.