In this paper, we consider the problem of recovering desired sound source signals from on-board microphone recordings on a noisy drone. Enhancement of source signal degraded by drone noise is considered to be a difficult task due to the strong noise generated from its motors and propellers causing an extremely low signal-to-drone noise ratio (SD‾NR). We propose a solution (i) by combining the widely known multichannel Wiener filter (MWF) to remove drone noise from microphone recordings, and (ii) further reduction of residual noise using a Gaussian mixture model (GMM) based dual-stage parametric Wiener filter (WF). The method exploits known statistics of motor current-specific drone noise. This combination of techniques to the specific context of signal enhancement for drone audition is applicable to irregular microphone arrays embedded on a drone enabling realistic integration to most drones. We demonstrate the validity of the proposed framework with extensive real data through (i) experimental recordings from two different drone acoustics datasets and (ii) outdoor measurements from a hovering drone for a bioacoustic application. The results confirm improved performance in terms of SD‾NR, speech quality (PESQ), and intelligibility (STOI) at very low SD‾NR (up to −30 dB) and show a strong potential for signal enhancement applications using noisy drones.