The restoration of particle number within Energy Density Functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and non-projected densities. As an alternative that might be advantageous for mass models, nuclear dynamics and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an Energy Density Functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.