Every club negotiate their shirt deals well in advance, do you think Liverpool or Arsenal made those deals in the last couple of weeks?
City had already won the title in 11/12, so you've added 1 more in 13/14, I'm not sure that'd make as significant a difference as that. Also, above I've compared you to Liverpool and Arsenal, 2 clubs nowhere near the top of y̶o̶u̶r̶ list you provided, which has you ranked above the likes of Chelsea and Barcelona.
Anyway, I'm happy to take that bet, just a minor change, I'll give you upto 5th biggest in the world at the time it's announced, on the condition that the shirt manufacturer are not based in the middle east.