Alternating Directions Method of Multipliers (ADMM) is a form of decomposition-coordination method that typically requires several iterations/communication rounds between the subproblems and the master problem to converge. Repeatedly solving the subproblems over several iterations add to the total computation time. Noting that the subproblems solved from one iteration to the next differs only by a few variables, this paper proposes a novel sensitivity-assisted ADMM framework for nonlinear programming (NLP) problems, where the subproblems are cheaply approximated using the parametric sensitivities. By exploiting the parametric sensitivities, the computation of the subproblems can be reduced to a single linear solve instead of solving the full NLP problem, thereby reducing the overall computation cost. Different algorithmic variations are discussed and demonstrated using two numerical examples.