  By analyzing 7.33\,fb$^{-1}$ of $e^+e^-$ collision data collected at
center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector,
we search for the semileptonic decays $D^+_s \to K_1(1270)^0 e^+\nu_e$ and
$D^+_s \to b_1(1235)^0 e^+\nu_e$ for the first time. No significant signals are
observed for either decay mode. The upper limits on the (product) branching
fractions are determined to be ${\mathcal B}[D^+_s \to K_1(1270)^0 e^+\nu_e] <
4.1\times 10^{-4}$ and ${\mathcal B}[D^+_s \to b_1(1235)^0 e^+\nu_e]\cdot
{\mathcal B}[b_1(1235)^0\to \omega\pi^0] < 6.4\times 10^{-4}$ at 90\%
confidence level.
