SKA-Low is a dense, uniform radio array that will enable high-precision studies of cosmic ray induced extensive air-showers. We are developing a near-field beam-forming or interferometric framework to reconstruct key air-shower parameters with the SKA-Low. In this work, we focus on the interferometric reconstruction of the arrival direction, shower core position, and the depth of shower maximum ($X_{\mathrm{max}}$), with the goal of extending the framework to reconstruct primary energy as well. The method has been developed on 100 PeV air-showers, simulated with CoREAS, for Proton, Helium, Carbon, Silicon and Iron primaries, for zenith angles 15°, 30° and 40° and achieved a universal calibration curve and an $X_{\mathrm{max}}$ resolution below 15 $\mathrm{g/cm^2}$ under realistic circumstances. We have also obtained an excellent angular resolution of 0.1° and a core resolution below 10 m. The interferometric framework can potentially extend the sensitivity of radio detection techniques down to PeV energies, which may significantly broaden the capabilities of the SKA-Low in cosmic-ray physics.