  Recent scanning tunnelling microscopy experiments in NbN thin disordered
superconducting films found an emergent inhomogeneity at the scale of tens of
nanometers. This inhomogeneity is mirrored by an apparent dimensional crossover
in the paraconductivity measured in transport above the superconducting
critical temperature $T_c$. This behavior was interpreted in terms of an
anomalous diffusion of fluctuating Cooper pairs, that display a {\em
quasi-confinement} (i.e., a slowing down of their diffusive dynamics) on length
scales shorter than the inhomogeneity identified by tunnelling experiments.
Here we assume this anomalous diffusive behavior of fluctuating Cooper pairs
and calculate the effect of these fluctuations on the electron density of
states above $T_c$. We find that the density of states is substantially
suppressed up to temperatures well above $T_c$. This behavior, which is closely
reminiscent of a pseudogap, only arises from the anomalous diffusion of
fluctuating Cooper pairs in the absence of stable preformed pairs, setting the
stage for an intermediate behavior between the two common paradigms in the
superconducting-insulator transition, namely the localisation of Cooper pairs
(the so-called bosonic scenario) and the breaking of Cooper pairs into unpaired
electrons due to strong disorder (the so-called fermionic scenario).
