In this paper, we discuss the application of abstract argumentation mechanisms to resources allocation. We show how such problems can be modeled as abstract argumentation frameworks, such that speci c sets of arguments corresponds to interesting solutions of the problem. By interesting solutions, here we mean Local Envy-Free (LEF) allocations. Envy-freeness is an important notion of fairness in resources allocation, assuming than no agent should prefer the resource allocated to another agent. We focus on LEF, a generalized form of envy-freeness, and we show that LEF allocations corresponds to some speci c sets of arguments in our argument-based modeling of the problem. This work in progress paves the way to richer connections between the various models of argumentation and resources allocation problems.