Context : EX Lup-type objects ( EXors ) are low-mass pre-main sequence objects characterized by optical and near-infrared outbursts attributed to highly enhanced accretion from the circumstellar disk onto the star . Aims : The trigger mechanism of EXor outbursts is still debated . One type of theory requires a close ( sub ) stellar companion that perturbs the inner part of the disk and triggers the onset of the enhanced accretion . Here , we study the radial velocity ( RV ) variations of EX Lup , the prototype of the EXor class , and test whether they can be related to a close companion . Methods : We conducted a five-year RV survey , collecting 54 observations with HARPS and FEROS . We analyzed the activity of EX Lup by checking the bisector , the equivalent width of the Ca 8662 Å line , the asymmetry of the Ca II K line , the activity indicator S _ { FEROS } , the asymmetry of the cross-correlation function , the line depth ratio of the VI/FeI lines , and the TiO , CaH 2 , CaH 3 , CaOH , and H \alpha indices . We complemented the RV measurements with a 14-day optical/infrared photometric monitoring to look for signatures of activity or varying accretion . Results : We found that the RV of EX Lup is periodic ( P = 7.417 d ) , with stable period , semi-amplitude ( 2.2 km s ^ { -1 } ) , and phase over at least four years of observations . This period is not present in any of the above-mentioned activity indicators . However , the RV of narrow metallic emission lines suggest the same period , but with an anti-correlating phase . The observed absorption line RVs can be fitted with a Keplerian solution around a 0.6 M _ { \odot } central star with M _ { 2 } \sin i = ( 14.7 \pm 0.7 ) M _ { Jup } and eccentricity of e = 0.24 . Alternatively , we attempted to model the observations with a cold or hot stellar spot as well . We found that in our simple model , the spot parameters needed to reproduce the RV semi-amplitude are in contradiction with the photometric variability , making the spot scenario unlikely . Conclusions : We qualitatively discuss two possibilities to explain the RV data : a geometry with two accretion columns rotating with the star , and a single accretion flow synchronized with the orbital motion of the hypothetical companion ; the second scenario is more consistent with the observed properties of EX Lup . In this scenario , the companion ’ s mass would fall into the brown dwarf desert , which , together with the unusually small separation of 0.06 AU would make EX Lup a unique binary system . The companion also has interesting implications on the physical mechanisms responsible for triggering the outburst .