We present Multi Unit Spectroscopic Explorer (MUSE) integral field spectroscopic observations of the host galaxy (PGC 043234) of one of the closest (z = 0.0206, D similar or equal to 90 Mpc) and best-studied tidal disruption events (TDEs), ASASSN-14li. The MUSE integral field data reveal asymmetric and filamentary structures that extend up to greater than or similar to 10 kpc from the post-starburst host galaxy of ASASSN-14li. The structures are traced only through the strong nebular [O III] lambda 5007, [N II] lambda 6584, and H alpha emission lines. The total off-nuclear [O III] lambda 5007 luminosity is 4.7 x 10(39) erg s(-1), and the ionized H mass is similar to 10(4) (500/n(e)) M-circle dot. Based on the Baldwin-Phillips-Terlevich diagram, the nebular emission can be driven by either AGN photoionization or shock excitation, with AGN photoionization favored given the narrow intrinsic line widths. The emission line ratios and spatial distribution strongly resemble ionization nebulae around fading AGNs such as IC 2497 (Hanny's Voorwerp) and ionization "cones" around Seyfert 2 nuclei. The morphology of the emission line filaments strongly suggest that PGC 043234 is a recent merger, which likely triggered a strong starburst and AGN activity leading to the post-starburst spectral signatures and the extended nebular emission line features we see today. We briefly discuss the implications of these observations in the context of the strongly enhanced TDE rates observed in post-starburst galaxies and their connection to enhanced theoretical TDE rates produced by supermassive black hole binaries.