Russia and Japan for sure. The third spot could be a total surprise, such as Uzbekistan, but I doubt it. I'd say Bulgaria, but Italy and Israel could take its place. Ukraine, Azerbaijan and Belarus would be the dark horses. Unless China has major upgrades, I believe they have no chance of getting a medal.
It's hard to predict anything else at this point because we still need to know which nations will qualify.
Europe: I don't think Spain will qualify. Turkey is more likely to qualify, but Germany, Finland or Estonia could also pull of a miraculous qualification. Of course, Ukraine might get the European quota, what means the WCh quota would be reallocated.
Americas: Mexico is the clear favorite here. US and Canada are its nearest rivals. Brazil has suffered with major problems and, now, I'd say we have no chance at all of qualifying.
Oceania: It's either Australia or New Zealand, but Australia has the edge. Still, either nation will be the weakest of the bunch.
Africa: I'm not sure if Egypt's qualification will be uphold because apparently two gymnasts from the group tested positive for doping. I don't think any other nation from Africa follows the minimum requirements for qualification, so we shall see what FIG will do.
Asia: Uzbekistan is the favorite for qualification. It's leaps and bounds ahead of the remaining countries available for a quota. South Korea and Kazakhstan are the only other nations which would be interested in the quota, but they are considerably behind Uzbekistan. Maybe Thailand would be interested too, who knows?