We present and theoretically analyse the performance of an innovative non-local superconducting single-photon detector. The device operates thanks to the energy-to-phase conversion mechanism, where the energy of the absorbed single-photon is transformed in a variation of the superconducting phase. To this scope, the detector is designed in the form of a double-loop superconductor/normal metal/superconductors (SNS) Josephson interferometer, where the detection occurs in a long SNS junction and the read-out is operated by a short SNS junction. The variation of the superconducting phase across the read-out junction is measured by recording the quasiparticle current flowing through a tunnel coupled superconducting probe. By exploiting realistic geometry and materials, the detector is able to reveal single-photons of frequency down to 10 GHz when operated at 10 mK. Furthermore, the device provides value of signal-to-noise ratio up 10^4 in the range 10 GHz-10 THz by selecting the magnetic flux and the bias voltage. This device can find direct applications as single-photon detector in both basic science and quantum technology, while the energy-to-phase conversion mechanism can be at the basis of non-local read-out and memory architectures for superconducting qubits.