The presence and properties of acoustic peaks near the nozzle of impinging rocket jets have been investigated. Four jets at a Mach number of 3.1 impinging on a plate at a distance L = 15r0, 20r0, 25r0 and 30r0 from the nozzle, where r0 is the nozzle radius, have been computed using large-eddy simulations. In all cases, upstream-travelling pressure waves are generated by the jet impingement on the plate, with amplitudes decreasing with the nozzle-to-plate distance. The near-nozzle pressure spectra contain peaks, at frequencies not varying much with this distance. For L ≥ 20r0, the spectra are dominated by a low-frequency peak, whereas two additional high-frequency peaks emerge for L = 15r0. The low-frequency peak is associated with the azimuthal mode nθ = 0, whereas the two other ones are due to strong components for modes nθ ≥ 1. As for near-nozzle tones for free and impinging jets at lower Mach numbers, the peak frequencies fall close to the frequency bands of the upstream-propagating guided jet waves, showing a link between the peaks and the latter waves. Regarding the peak levels, they do not change significantly with the nozzle-to-plate distance for the low-frequency peak, but they decrease by 1.5 to 18 dB as the distance increases for the other peaks. Finally, for L ≥ 20r0, the near-nozzle peak frequency is close to that of the strongest shear-layer structures, indicating a connexion between the upstream noise and these structures. For L = 15r0, a shock-leakage mechanism of a near-plate shock is found to generate the upstream noise.