Almaty will be it. Nursultan the Great will not spare expense.
That is going to be a problem with Winter Games: there are very few Eastern despoties where they could be held. Russia, China, Kazakhstan, Belarus, may be Azerbaijan and...? North Korea would work climatically - but will be boycotted.
It seems to me that every Central Asian state would work except perhaps Uzbekistan.
Kyrgyzstan might have the location, but will never have a dictatorship strong enough to pull it of. Tajikistan has the dictatorship but locations would have to be too remote. Neither of them would have either money or fan base to attempt it, anyway. Turkmenistan I am not even sure has any locations - though it is perfect as far as being a dictatorship is concerned. But, then, it might be too perfect a dictatorship to ever get it. Uzbekistan might, actually, work.