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We propose a new method to incorporate statistical priors on the solution of the nonnegative matrix factorization (NMF) for single-channel source separation (SCSS) applications. The Gaussian mixture model (GMM) is used as a log-normalized gain prior model for the NMF solution. The normalization makes the prior models energy independent. In NMF based SCSS, NMF is used to decompose the spectra of the observed mixed signal as a weighted linear combination of a set of trained basis vectors. In this work, the NMF decomposition weights are enforced to consider statistical prior information on the weight combination patterns that the trained basis vectors can jointly receive for each source in the observed mixed signal. The NMF solutions for the weights are encouraged to increase the log likelihood with the trained gain prior GMMs while reducing the NMF reconstruction error at the same time.