Channel state information (CSI) estimation is a critical issue in the design of modern massive multiple-input multiple-output (mMIMO) networks. With the increasing number of users, assigning orthogonal pilots to everyone incurs a large overhead that strongly penalizes the system's spectral efficiency (SE). It becomes thus necessary to reuse pilots, giving rise to pilot contamination, a vital performance bottleneck of mMIMO networks. Reusing pilots among the users of the same cell is a desirable operation condition from the perspective of reducing training overheads; however, the intra-cell pilot contamination might worsen due to the users' proximity. Reconfigurable intelligent surfaces (RISs), capable of smartly controlling the wireless channel, can be leveraged for intra-cell pilot reuse. In this paper, our main contribution is a RIS-aided approach for intra-cell pilot reuse and the corresponding channel estimation method. Relying upon the knowledge of only statistical CSI, we optimize the RIS phase shifts based on a manifold optimization framework and the RIS positioning based on a deterministic approach. The extensive numerical results highlight the remarkable performance improvements the proposed scheme achieves (for both uplink and downlink transmissions) compared to other alternatives.