It was recently shown that, taking into account the granular structure of graphene lattice, the Dirac-like dynamics of its quasiparticles resists beyond the lowest energy approximation. This can be described in terms of new phase-space variables, $(\overrightarrow{X},\overrightarrow{P})$, that enjoy generalized Heisenberg algebras. In this letter, we add to that picture the important case of noncommuting $\overrightarrow{X}$, for which $[X^i,X^j]=i{\theta }^{ij}$ and we find that ${\theta }^{ij}={\ell }^2{ϵ}^{ij}$, with ℓ the lattice spacing. We close by giving both the general recipe and a possible specific kinematic setup for the practical implementation of this approach to test noncommutative theories in tabletop analog experiments on graphene.