The advances in fluorescent diamond-based magnetic field sensors have led this technology into the field of fiber optics. Recently, devices employing diamond nanobeams or diamond chips embedded on an optical fiber tip enabled achieving fT-level sensitivities. Nevertheless, these demonstrations were still confined to operation over localized magnetic field sources. A new approach of volumetric incorporation of nanodiamonds into the optical fiber core enables optical fibers sensitive to magnetic field at any point along the fiber length. We show that information on the perturbed spin state of a diamond nitrogen-vacancy color center can be transmitted over a macroscopic length in an optical fiber, in presence of noise from large concentration of the color centers along the fiber. This is exploited in optical readout at the fiber output not only of the magnetic field value, but also spatially variable information on the field, which enables the localization of its source.