Enhanced magnetism has recently been reported for the topological-insulator/ferromagnet interface ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$/EuS with Curie temperatures claimed to be raised above room temperature from the bulk EuS value of 16 K. Here we investigate the analogous interface ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$/EuSe. EuSe is a low-temperature layered ferrimagnet that is particularly sensitive to external perturbations. We find that superconducting quantum interference device (SQUID) magnetometry of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$/EuSe heterostructures reveals precisely the magnetic phase diagram known from EuSe, including the ferrimagnetic phase below 5 K, without any apparent changes from the bulk behavior. Choosing a temperature of 10 K to search for magnetic enhancement, we determine an upper limit for a possible magnetic coercive field of 3 mT. Using interface sensitive x-ray absorption spectroscopy we verify the magnetic divalent configuration of the Eu at the interface without contamination by ${\mathrm{Eu}}^{3+}$, and by x-ray magnetic circular dichroism (XMCD) we confirm at the interface the magnetic hysteresis obtained by SQUID. XMCD data obtained at 10 K in a magnetic field of 6 T indicate a magnetic spin moment of ${m}_{z,\mathrm{spin}}=7\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{B}/{\mathrm{Eu}}^{2+}$, in good agreement with the SQUID data and the expected theoretical moment of ${\mathrm{Eu}}^{2+}$. Subsequent XMCD measurements in zero field show, however, that sizable remanent magnetization is absent at the interface for temperatures down to about 10 K.