What does nonnegative zero-phase response mean?
What they mean here is that the real-valued amplitude function of the linear phase FIR filter that you provide to the function must be non-negative, because it is interpreted as the desired squared magnitude of the minimum-phase filter. This amplitude function is referred to as zero-phase response, which is the frequency response of the filter when the coefficients are shifted such that they are centered around the origin, i.e., $b[n]=b[-n]$ is satisfied. Note that the filter length must be odd.
If $N$ is the (odd) filter length, the zero-phase response is given by
$$B_{zp}(e^{j\omega})=B(e^{j\omega})e^{j\omega(N-1)/2}$$
where $B(e^{j\omega})$ is the frequency response of the causal filter.