Context: .Free-floating planetary-mass objects have masses below the deuterium burning mass limit at about 13 Jupiter masses, and have mostly been found in very young open clusters. Their origin and relationship to stars and brown dwarfs are still a mystery. Aims: .The recent detection by direct imaging of three giant planets at wide separation (50-250 AU) from their primaries has raised the question about the true "isolation" of planetary-mass objects in clusters. Our goal was to test the possibility that some free-floating planetary-mass objects could in fact be part of wide planetary systems. Methods: .We searched in the literature for stellar and brown-dwarf candidates members of the σ Orionis cluster (~3 Ma, ~360 pc) at small angular separations from published candidate planetary-mass objects. We found one candidate planetary system composed of an X-ray source, SE 70, and a planetary-mass object, S Ori 68, separated by only 4.6 arcsec. In order to assess the cluster membership of the X-ray source, we obtained mid-resolution optical spectroscopy using ISIS on the William Herschel Telescope. We also compiled additional data on the target from available astronomical catalogues. Results: .We have found that SE 70 follows the spectrophotometric sequence of the cluster and displays spectroscopic features of youth, such as lithium in absorption and chromospheric Hα emission. The radial velocity is consistent with cluster membership. Hence, SE 70 is very probably a member of the σ Orionis cluster. The projected physical separation between SE 70 and S Ori 68 is 1700~± 300 AU at the distance of the cluster. If a common proper motion is confirmed in the near future, the system would be composed of an M5-6 brown dwarf with an estimated mass of ~45 M_Jup and an L5 ± 2 giant planet with an estimated mass of ~5 M_Jup. It would be the widest and one of the lowest-mass planetary systems known so far.