  We consider the minimal seesaw model in which two gauge singlet right handed
neutrinos with opposite lepton numbers are added to the Standard Model. In this
model, the smallness of the neutrino mass is explained by the tiny lepton
number violating coupling between one of the singlets with the standard
left-handed neutrinos. This allows one to have the right handed neutrino mass
at the TeV scale as well as appreciable mixing between the light and heavy
states. This model is fully reconstructible in terms of the neutrino
oscillation parameters apart from the overall coupling strengths. We show that
the overall coupling strength $y_\nu$ for the Dirac type coupling between the
left handed neutrino and one of the singlets can be restricted by consideration
of the (meta)stability bounds on the electroweak vacuum. In this scenario the
lepton flavor violating decays of charged leptons can be appreciable which can
put further constraint on $y_\nu$, for right-handed neutrinos at TeV scale. We
discuss the combined constraints on $y_\nu$ for this scenario from the process
$\mu \rightarrow e \gamma$ and from the consideration of vacuum (meta)stability
constraints on the Higgs self coupling. We also briefly discuss the
implications for neutrinoless double beta decay and possible signatures of the
model that can be expected at colliders.
