In this letter, we propose new trainable Fast Fourier Transform (FFT) structures to increase the accuracy of beamspace transformation in the multi-user (MU) mode of Massive Multiple Input Multiple Output (MIMO) receiver. The FFT is a widely employed beamspace transformation technique, thanks to its low transforming complexity. Unfortunately, there is a significant performance loss of MU signal detection in the FFT beamspace, as default FFT beams are not co-directed with angles of arrivals. We address this issue with trainable FFT that outperforms not only fixed FFT approaches, but also other trainable FFT techniques.