Early-type galaxies show a strong size evolution with redshift. This evolution is explained by fast in-situ star formation at high-$z$ followed by a late mass assembly mostly driven by minor mergers that deposit stars primarily in the outer halo. We aim to identify structural components of the Hydra I cD galaxy NGC 3311 to investigate the connection between the central galaxy and the surrounding stellar halo. We map the line-of-sight velocity distribution (LOSVD) using MUSE pointings covering NGC 3311 out to $25$ kpc. Combining photometric and spectroscopic data, we model the LOSVD maps using a finite mixture distribution, including four non-concentric, nearly isothermal spheroids, with different line-of-sight systemic velocities $V$, velocity dispersions $sigma$, and higher order Gauss-Hermite moments $h_3$ and $h_4$. The comparison of the correlations between $h_3$ and $h_4$ with $V/sigma$ with simulations indicates that NGC 3311 assembled mainly through dry mergers. The $sigma$ profile rises to $simeq 400$ km s$^{text -1}$ at 20 kpc 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$^{text{-1}}$) 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 ($Delta V = 204$ kms$^{-1}$), but coincide with the cluster core X-ray isophotes and the mean velocity of galaxies. Also, the envelope contributes to the broad wings of the LOSVD measured by large $h_4$ within 10 kpc. 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.
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