Nitrogen-bearing molecules display variable isotopic fractionation levels in different astronomical environments such as in the interstellar medium or in the Solar system. Models of interstellar chemistry are unable to induce nitrogen fraction in cold molecular clouds as exchange reactions for 15N are mostly inefficient. Here, we developed a new gas-grain model for nitrogen fractionation including a thorough search for new nitrogen fractionation reactions and a realistic description of atom depletion on to interstellar dust particles. We show that, while dense molecular cloud gas-phase chemistry alone leads to very low fractionation, 14N atoms are preferentially depleted from the gas phase due to a mass-dependent grain surface sticking rate for atomic nitrogen. However, assuming an elementary 14N/15N ratio of 441 (equal to the solar wind value), our model leads to only low 15N enrichment for all N-containing species synthesized in the gas phase with predicted 14N/15N ratios in the range 360-400. Higher enrichment levels can neither be explained by this mechanism, nor through chemistry, with two possible explanations: (i) The elementary 14N/15N ratio in the local ISM is smaller, as suggested by the recent work of Romano et al., with a hypothetic 15NNH+ and 15NNH+ depletion due to variation of the electronic recombination rate constant variation with the isotopes and (ii) N2 photodissociation leads to variable nitrogen fractionation in diffuse molecular clouds where photons play an important role, which is conserved during dense molecular cloud formation as suggested by the work of Furuya & Aikawa.< Réduire