We generalize the initial steps of the Faddeev-Reshetikhin procedure to the AdS5 ×S5 superstring theory. Specifically, we propose a modification of the Poisson bracket whose alleviated non-ultralocality enables to write down a lattice Poisson algebra for the Lax matrix. We then show that the dynamics of the Pohlmeyer reduction of the AdS5 × S5 superstring can be naturally reproduced with respect to this modified Poisson bracket. This work generalizes the alleviation procedure recently developed for symmetric space σ- models. It also shows that the lattice Poisson algebra recently obtained for the AdS5 ×S5 semi-symmetric space sine-Gordon theory coincides with the one obtained by the alleviation procedure.