Massive multiple-input multiple-output (MIMO) is expected to play a central role in future wireless systems. The deployment of large antenna arrays at the base station and the mobile users offers multiplexing and beamforming gains that boost system spectral efficiency. Unfortunately, the high cost and power consumption of components like analog-to-digital converters makes assigning an RF chain per antenna and applying typical fully digital precoding/combining solutions difficult. In this paper, a novel architecture for massive MIMO receivers, consisting of arrays of switches and constant (non-tunable) phase shifters, is proposed. This architecture applies a quasi-coherent combining in the RF domain to reduce the number of required RF chains. An algorithm that designs the RF combining for this architecture is developed and analyzed. Results show that the proposed massive MIMO combining model can achieve a comparable performance to the fully-digital receiver architecture in single-user and multi-user massive MIMO setups.