A system is identifiable if there exists a unique relationship between its input-output behaviour and the parameter values. Differential-Algebraic Equation (DAE) systems have an input-output behaviour that is described by a parameterized set of ordinary differential and algebraic equations. Methods proposed in the literature to test the identifiability of DAE systems are based on the tools of differential algebra and rely on time-differentiation of model equations. As a result, even when dealing with a few states and parameters, the calculations required for these methods may become intractable. An alternative, which we propose, is to linearize the non-linear DAE system about some rest point and then test the identifiability properties of the linearized system. In this work, we show that strong local identifiability of the linearized DAE system provides a sufficient condition for the strong local identifiability of the original non-linear DAE system.