Since very few Type-I superconductors are known and most are elemental superconductors, there are very few experimental platforms where the interaction between Type-I superconductivity and topologically nontrivial band structure can be probed. The rhenium aluminide Al$_6$Re has recently been identified as a Type-I superconductor with a transition of 0.74,K and a critical field of $sim$50,Oe. Here, we report its magnetotransport behavior including de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations. Angular dependence of the magnetoresistance reveals a highly anisotropic Fermi surface with dominant hole character. From the strong oscillatory component $Delta R_{xx}$ in high magnetic fields up to 33,T, the Landau index infinite-field intercept in the case of a single oscillation frequency, and the phase factor $varphi$ where multiple frequencies coexist, are both $sim$1/4. This intermediate value is suggestive of possible nontrivial band topology but does not allow strong conclusions.
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