  We report on ac magnetic susceptibility measurements under pressure of the
Au-Al-Yb alloy, a crystalline approximant to the icosahedral quasicrystal that
shows unconventional quantum criticality. In describing the susceptibility as
$\chi(T)^{-1} - \chi(0)^{-1} \propto T^{\gamma}$, we find that $\chi(0)^{-1}$
decreases with increasing pressure and vanishes to zero at the critical
pressure $P_{\rm c} \simeq 2$ GPa, with $\gamma~ (\simeq 0.5)$ unchanged. We
suggest that this quantum criticality emerges owing to critical valence
fluctuations. Above $P_{\rm c}$, the approximant undergoes a magnetic
transition at $T \simeq 100$ mK. These results are contrasted with the fact
that, in the quasicrystal, the quantum criticality is robust against the
application of pressure. The applicability of the so-called $T/H$ scaling to
the approximant is also discussed.
