  The description of the hadron production at very forward rapidities and low
transverse momentum is usually made using phenomenological models based on
nonperturbative physics. However, at high energies and large rapidities the
wave function of one of the projectiles is probed at very small Bjorken $x$,
being characterized by a large number of gluons. In this kinematical regime, a
new state of matter - the Color Glass Condensate (CGC) - is expected to be
formed. One the main characteristics of such system is the presence of a new
dynamical momentum scale, the saturation scale $Q_s$, which can assume values
very larger than the QCD confinement scale $\Lambda_{QCD}$ and give the scale
of the running coupling constant. In this paper we assume that in particular
kinematical region probed by LHC forward (LHCf) experiment the saturation scale
can be considered the hard momentum scale present in the process and calculate
the forward neutral pion production at very low-$p_T$ using a perturbative
approach. We demonstrate that the CGC formalism is able to successfully
describe the LHCf data, which can be considered as a compelling indication of
the presence of non-linear QCD effects at LHC energies.
