The influence of a Nonlinear Tuned Vibration Absorber (NLTVA) on the airfoil flutter is investigated. In particular, its effect on the instability threshold and the potential subriticality of the bifurcation is analyzed. For that purpose, the airfoil is modeled using the classical pitch and plunge aeroelastic model together with a linear approach for the aerodynamic loads. To ensure limit cycle oscillation (LCO) to the airfoil in its post-critical regime, cubic nonlinearities are added to the structural model. The influence of each NLTVA parameter is studied and an optimum tuning of these parameters is found. The study reveals the ability of the NLTVA to both shift the instability and avoid its possible subcriticality.