Context.Early-type galaxies (ETGs) show a strong size evolution with redshift. This evolution is explained by fast “in-situ” star formation at high-zfollowed by a late mass assembly mostly driven by minor mergers that deposit stars primarily in the outer halo.Aims.We aim to identify the main structural components of the Hydra I cD galaxy NGC 3311 to investigate the connection between the central galaxy and the surrounding stellar halo.Methods.We produce maps of the line-of-sight velocity distribution (LOSVD) moments from a mosaic of MUSE pointings covering NGC 3311 out to 25 kpc. Combining deep photometric and spectroscopic data, we model the LOSVD maps using a finite mixture distribution, including four non-concentric components that are nearly isothermal spheroids, with different line-of-sight systemic velocitiesV, velocity dispersionsσ, and small (constant) values of the higher order Gauss-Hermite momentsh₃andh₄.Results.The kinemetry analysis indicates that NGC 3311 is classified as a slow rotator, although the galaxy shows a line-of-sight velocity gradient along the photometric major axis. The comparison of the correlations betweenh₃andh₄withV/σwith simulated galaxies indicates that NGC 3311 assembled mainly through dry mergers. Theσprofile rises to ≃ 400 km s^-1at 20 kpc, a significant fraction (0.55) of the Hydra I cluster velocity dispersion, indicating that stars there were stripped from progenitors orbiting in the cluster core. The finite mixture distribution modeling supports three inner components related to the central galaxy and a fourth component with large effective radius (51 kpc) and velocity dispersion (327 km s^-1) consistent with a cD envelope. We find that the cD envelope is offset from the center of NGC 3311 both spatially (8.6 kpc) and in velocity (ΔV= 204 km s^-1), but coincides with the cluster core X-ray isophotes and the mean velocity of core galaxies. Also, the envelope contributes to the broad wings of the LOSVD measured by largeh₄values within 10 kpc.Conclusions.The cD envelope of NGC 3311 is dynamically associated with the cluster core, which in Hydra I is in addition displaced from the cluster center, presumably due to a recent subcluster merger.