Context : Central galaxies in galaxy clusters may be key discriminants in the competition between the cold dark matter ( CDM ) paradigm and modified Newtonian dynamics ( MOND ) . Aims : We investigate the dark halo of NGC 1399 , the central galaxy of the Fornax cluster , out to a galactocentric distance of 80 kpc . Methods : The data base consists of 656 radial velocities of globular clusters obtained with MXU/VLT and GMOS/Gemini , which is the largest sample so far for any galaxy . We performed a Jeans analysis for a non-rotating isotropic model . Results : An NFW halo with the parameters r _ { s } = 50 kpc and \varrho _ { s } = 0.0065 M _ { \odot } / pc ^ { 3 } provides a good description of our data , fitting well to the X-ray mass . More massive halos are also permitted that agree with the mass of the Fornax cluster as derived from galaxy velocities . We compare this halo with the expected MOND models under isotropy and find that additional dark matter on the order of the stellar mass is needed to get agreement . A fully radial infinite globular cluster system would be needed to change this conclusion . Conclusions : Regarding CDM , we can not draw firm conclusions . To really constrain a cluster wide halo , more data covering a larger radius are necessary . The MOND result appears as a small-scale variant of the finding that MOND in galaxy clusters still needs dark matter .