Models with gauge symmetry $SU(3{)}_{c}\ensuremath{\bigotimes}SU(3{)}_{L}\ensuremath{\bigotimes}U(1{)}_{N}$ have different candidates for dark matter, for example, a heavy neutral fermion interacting with standard model particles through different mediators, scalar and vector portals. At the same time, these portals can produce signals in the anomalous magnetic moment of the muon that violate the present bounds on this quantity. Combining the requirement to have a dark matter candidate in the $SU(3{)}_{c}\ensuremath{\bigotimes}SU(3{)}_{L}\ensuremath{\bigotimes}U(1{)}_{N}$ model with heavy neutral leptons and to explain the anomalous magnetic moment of the muon we set constraints on the highest symmetry breaking scale of the model. These bounds are competitive with the constraints from LHC and set a favored region that can also be tested in future direct detection experiments, such as the LUX-ZEPLIN (LZ) experiment.