We use far-infrared (FIR) dust polarimetric data from HAWC+/SOFIA at 53 micron to study the magnetic field orientations in the starburst galaxy Messier 82 (M82). Combining the analysis of polarization-angle dispersion with the traditional Davis-Chandrasekhar-Fermi (DCF) method, a plane-of-sky (POS) magnetic field strength of BPOS ~ 1.0 mG is estimated. However, considering that in the M82 the bulk of polarized dust emission is located within the outflow-dominated region, the BPOS is overestimated by the presence of large-scale flows. Thus, a modification to the DCF method was performed and a corrected BPOS ~ 0.8 mG was estimated. Using the estimated magnetic field strength and energy balance considerations, we construct a two-dimensional map of BPOS that resembles the FIR surface brightness distribution. Finally, using this map and the estimated magnetic field orientations, we are able to construct and visualize the magnetic fields to radial distances of ~ 5 kpc. We find that a large volume of the magnetic fields in the galactic outflow of M82 can be considered as force-free with a dipole-like overall appearance. With this extended magnetic field structure we will be able to determine whether the magnetic field is strong enough to form close field lines facilitating feedback from/to the ongoing star formation, or open field lines magnetizing the intergalactic medium.