There are two possibilities:
- If you're referring to the off-chance that it may rain, for example when planning to wash your car, then you would say something like:
I want to wash my car, but I don't know that it won't rain.
Here the speaker is hesitant to start washing the car for fear that it will start to rain.
- If you're referring to knowledge of impending rain, then you could say:
A: Why are you washing the car?
B: You said it wasn't going to rain.
A: I don't know whether it isn't going to rain.
Note that although this is grammatically correct, it's highly uncommon and clumsy. At least to my ear, "whether" in itself already contains the "or not," i.e. the negative polarity which includes the option of something NOT happening, so there is no need to express it outright. The speaker would more than likely simply say:
I don't know whether it's going to rain.
Although "whether" is correct, I personally never use it in conversation - I always use "if" as do most of the people I know.