Since the Standard Model cannot describe the observed baryon asymmetry or dark matter density in the universe, many models of New Physics introduce heavy neutrinos as an explanation for these effects. Such heavy Dirac or Majorana neutrinos could be produced at future linear $e^+e^-$ colliders, such as the Compact LInear Collider (CLIC) or the International Linear Collider (ILC). We analysed the possibility of observing the production and decay of the heavy neutrinos in the $qql$ final state at ILC running at 500 GeV and 1 TeV and CLIC running at 3 TeV. In tne analysis, the event generation was based on Whizard and fast simulation of the detector response was performed with DELPHES. Both Dirac and Majorana neutrinos with masses from 200 GeV to 3.2 TeV were considered. Estimated limits on the production cross sections and on the neutrino-lepton coupling were compared with the current CMS limits, as well as the projected limits coming from future hadron colliders. The obtained results are more stringent than any other limit estimate published so far.