Astrophysical neutrinos with energies higher than $E_\nu>10\,\mathrm{PeV}$ have not been measured yet, therefore, we do not know what kind of sources are contributing to this high energy neutrino flux. Concretely, we are interested in testing the hypothesis in which we have a hidden contribution coming from the decay of heavy dark matter particles.

The first neutrino radio telescopes will be constructed during the following decade, having as a principal goal the detection of the cosmogenic neutrinos, and being able to disentangle the principal source contributing at these high energies for the astrophysical neutrino flux. In this work we study the projected sensitivity of up-coming neutrino radio telescopes, such as RNO-G, GRAND and IceCube-Gen2 radio array, to decaying dark matter scenarios. We perform a forecast analysis in order to place conservative constraints on the lifetime of dark matter within the range $m_\mathrm{DM}=[10^7-10^{15}]\,\mathrm{GeV}$ after assuming the dominant astrophysical neutrino source, the one that will act as our background for the hidden dark matter signal. These forecasted limits open a new parameter space for some decaying channels, and complement the limits obtained for the $b$ channel due to its multi-messenger agreement.