With the aim of contributing to the understanding of the disk formation process in Be stars, we pursued a one-year spectroscopic observing campaign of the Be star {mu} Centauri in the L-band, using VLT/ISAAC. We present the nine near-IR spectra we obtained in an epoch of relative photometric quiescence prior to an outburst of {Delta}V=0.4 magnitude. Visual estimates during the epoch of our L-band spectroscopy are also presented for the first time, together with the unpublished complete visual light curve between the years 1998 and 2014. We observe significant and monotonic changes in emission line strength of Bracket-{alpha} and Pfund-{gamma} lines relative to Humphreys lines, and also in the continuum slope. We interpret these observed changes in terms of important changes to the column density of the line emitting regions, moving from an optically thin to an optically thick stage just prior to a major outburst. For each observing date, we provide estimates for the column density and relative extension of the line emitting region. If the changes observed toward the end of our observing campaign were related to mass-loss changes from the central star, they would correspond to an increase in a factor of two in the mass of the disk in the innermost region. If related to the visual outburst observed one month later, the variability observed in our spectra would be the first detection of the early disk formation process in the L-band.