Supermassive black hole (SMBH) binaries are difficult to differentiate from a single massive black hole using electromagnetic data because of their small orbital separation (they are unresolved in most cases) and because of the uncertainties about the uniqueness of their observational signatures. Thus, numerical simulations are a key step to identify observational signatures of SMBH binaries that might be searched for in future datasets (in particular in the soft X-ray domain). In this study, we focus on gravitationally bound SMBHs during the first stages of their coalescence. In the simulations performed with the open-source code AMRVAC, we are looking at the gravitational influence of a secondary SMBH on the accretion disc of a primary SMBH. Among other features, the gravitational influence of the second SMBH creates a spiral in the disc. Previous studies showed that spiral waves in a disc could be imprinted in the shape of the iron K-alpha emission line, which could be detected with high resolution X-ray spectroscopy. Thus, the X-IFU spectrometer onboard Athena may be a very important facility to diagnose the presence of a SMBH binary at the center of a galaxy in the first stages of its coalescence by resolving the shape of the iron K-alpha emission line. In this work, we compute the shape of the K-alpha emission line using an analytical model based on simulations of discs prone to the gravity of both a primary and secondary black hole. This allows us to study the potential detectability of such a spiral wave and the associated population of binary systems (in terms of mass ratio, distance, orbital separation, …) that could potentially be detected with X-IFU.