We calculate the flavor-singlet contribution to the $Btoeta^{(prime)}$ transition form factors from the gluonic content of the $eta^{(prime)}$ meson in the large-recoil region using the perturbative QCD approach. The formulation for the $eta$-$eta$ mixing in the quark-flavor and singlet-octet schemes is compared, and employed to determine the chiral enhancement scales associated with the two-parton twist-3 $eta^{(prime)}$ meson distribution amplitudes. It is found that the gluonic contribution is negligible in the $Btoeta$ form factors, and reaches few percents in the $Btoeta$ ones. Its impact on the accommodation of the measured $Btoeta^{(prime)} K$ branching ratios in the perturbative QCD and QCD-improved factorization approaches is elaborated.
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