  We investigate a new method to recover (if any) a possible varying speed of
light (VSL) signal from cosmological data. It comes as an upgrade of [1,2],
where it was argued that such signal could be detected at a single redshift
location only. Here, we show how it is possible to extract information on a VSL
signal on an extended redshift range. We use mock cosmological data from future
galaxy surveys (BOSS, DESI, \emph{WFirst-2.4} and SKA): the sound horizon at
decoupling imprinted in the clustering of galaxies (BAO) as an angular diameter
distance, and the expansion rate derived from those galaxies recognized as
cosmic chronometers. We find that, given the forecast sensitivities of such
surveys, a $\sim1\%$ VSL signal can be detected at $3\sigma$ confidence level
in the redshift interval $z \in [0.,1.55]$. Smaller signals $(\sim0.1\%)$ will
be hardly detected (even if some lower possibility for a $1\sigma$ detection is
still possible). Finally, we discuss the degeneration between a VSL signal and
a non-null spatial curvature; we show that, given present bounds on curvature,
any signal, if detected, can be attributed to a VSL signal with a very high
confidence. On the other hand, our method turns out to be useful even in the
classical scenario of a constant speed of light: in this case, the signal we
reconstruct can be totally ascribed to spatial curvature and, thus, we might
have a method to detect a $0.01$-order curvature in the same redhift range with
a very high confidence.
