I am trying to say "I am not feeling hunger at the moment, but I probably will in the nearest future." "I am not starving yet" - is that a proper English in general and particularly in that case of usage?
Yes, it is correct, albeit slightly informal. More formally you would say I am not hungry yet.
You could also say something like:
A: I'm hungry!
B: How hungry are you?
A: Well I'm not starving just yet.