Wiener filtering is one of the most ubiquitous tools in signal processing, in particular for signal denoising and source separation. In the context of audio, it is typically applied in the time-frequency domain by means of the short-time Fourier transform (STFT). Such processing does generally not take into account the relationship between STFT coefficients in different time-frequency bins due to the redundancy of the STFT, which we refer to as \emph{consistency}. We propose to enforce this relationship in the design of the Wiener filter, either as a hard constraint or as a soft penalty. We derive two conjugate gradient algorithms for the computation of the filter coefficients and show improved audio source separation performance compared to the classical Wiener filter both in oracle and in blind conditions.