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 , we find that decreases with increasing pressure and vanishes to zero at the critical pressure GPa, with unchanged. We suggest that this quantum criticality emerges owing to critical valence fluctuations. Above , the approximant undergoes a magnetic transition at 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 scaling to the approximant is also discussed.

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