No. The probability of an event is never, ever negative, even in quantum. We use the complex scalar product, c x c^*, to get probabilities, and those are necessarily positive even for complex numbers. The same is true for the generalization to functions required in quantum mechanics.

If your wave function at point (0,0,0) were i x delta(0) (i.e. a point-like particle perfectly located at the three-dimensional origin), the probability of finding the particle there isn't i^2, but i x i^* = i x (-i) = 1.