In multi-user multiple-input multiple-output (MU-MIMO) systems, the non-linear behavior of the power amplifiers (PAs) may cause degradation of the linear precoding schemes dealing with interference between user equipments (UEs), e.g., the zero-forcing (ZF) precoder. One way to minimize this effect is to use digital-pre-distortion (DPD) modules to linearize the PAs. However, using perfect DPD modules is costly and it may incur significant power consumption. As an alternative, we consider the problem of characterizing non-linearity-aware ZF (NLA-ZF) precoding schemes, hereby defined as linear precoders that achieve perfect interference cancellation in the presence of PA non-linearity by exploiting knowledge of this non-linear response. We provide initial iterative solutions that allow achieving NLA-ZF (up to adjustable tolerance) in a two-UE downlink MU-MIMO scenario where the base station (BS) has an even number of antennas, and each antenna is connected to a PA exhibiting third-order memory-less non-linear behavior. The proposed approach allows for performance gains in scenarios with significant residual interference.