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 ...