  The family of the endohedral gallide cluster compounds recently emerged as a
new family of superconductors which is expected to host systems displaying
unconventional physics. Mo$_8$Ga$_{41}$ is an important member of this family
which shows relatively large $T_c \sim$ 10 K and has shown indications of
strong electron-phonon coupling and multi-band superconductivity. Here, through
direct measurement of superconducting energy gap by scanning tunneling
spectroscopy (STS) we demonstrate the existence of two distinct superconducting
gaps of magnitude 0.85 meV and 1.6 meV respectively in Mo$_8$Ga$_{41}$. Both
the gaps are seen to be conventional in nature as they evolve systematically
with temperature as per the predictions of BCS theory. Our band structure
calculations reveal that only two specific Mo sites in an unit cell contribute
to superconductivity where only $d_{xz}$/$d_{yz}$ and $d_{x^2-y^2}$ orbitals
have strong contributions. Our analysis indicates that the site-elective
contribution govern the two-gap nature of superconductivity in Mo$_8$Ga$_{41}$.
