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In the central region of the galaxy cluster Abell 2199 (A2199) resides the cD galaxy NGC 6166, which spatially coincides with the 3C 338 radio source. Lobes, jets, and a more detached southern structure (similar to a jet labelled as ridge) are seen at kiloparsec-scale images of 3C 338. This unusual radio morphology has led to the proposition of different hypotheses about its physical origin in the literature. In this work, we study the feasibility of a dynamical scenario where NGC 6166 moves around the X-ray inferred centre of A2199 from the point of view of three-dimensional hydrodynamic simulations. The physical characteristics of the intra-cluster medium in which the jet propagates are constrained to those derived from X-ray observations in the vicinity of NGC 6166. Possible orbits for the jet inlet region are derived from the estimated radial velocity of NGC 6166, while the jet parameters are constrained by parsec-scale interferometric radio observations and the estimated jet power of 3C 338 obtained from radio and X-ray data. Our results show that the hypothesis of NGC 6166 has been moving around the centre of A2199 during the last tens of million of years is compatible with the general radio morphology of 3C 338. Furthermore, the proposed dynamic scenario for the motion of NGC 6166 may be linked to gravitational perturbations induced by the passage of a sub-cluster of galaxies hundreds of millions of years ago., Comment: 26 pages, 24 figures