Observers are usually formulated as explicit systems of differential equations and implemented using standard ODE solvers. In this paper, we show that there can be advantages in formulating the observer as a DAE (Differential-Algebraic Equation). A canonical DAE observer is proposed and it is shown that it can be implemented using standard DAE solvers. The DAE implementation of the observer can be considered regardless of the design philosophy used (extended linearization, Lyapunov based, Lie algebraic, ...). We present a simple design strategy for this canonical DAE observer based on the extended-linearization method.