There have been many speculations about the presence of cosmic ray protons (CRps) in galaxy clusters over the past two decades. However, no direct evidence such as the characteristic γ-ray signature of decaying pions has been found so far. These pions would be a direct tracer of hadronic CRp interactions with the ambient thermal gas also yielding observable synchrotron and inverse Compton emission by additionally produced secondary electrons. The obvious question concerns the type of galaxy clusters most likely to yield a signal: Particularly suited sites should be cluster cooling cores due to their high gas and magnetic energy densities. We studied a nearby sample of clusters evincing cooling cores in order to place stringent limits on the cluster CRp population by using non-detections of EGRET. In this context, we examined the possibility of a hadronic origin of Coma-sized radio halos as well as radio mini-halos. Especially for mini-halos, strong clues are provided by the very plausible small amount of required CRp energy density and a matching radio profile. Introducing the hadronic minimum energy criterion, we show that the energetically favored CRp energy density is constrained to 2%± 1% of the thermal energy density in Perseus. We also studied the CRp population within the cooling core region of Virgo using the TeV γ-ray detection of M 87 by HEGRA. Both the expected radial γ-ray profile and the required amount of CRp support this hadronic scenario.