Approximating the set of terms reachable by rewriting finds more and more applications ranging from termination proofs of term rewriting systems, cryptographic protocol verification to static analysis of programs. For such applications, the precision of the approximation is crucial. However, such approximations are coarse when the rewriting system is used under a specific strategy. This is due to the fact that techniques approximating reachable terms do not take rewriting strategies into account. Thus, they produce approximations containing terms that are not reachable w.r.t. the rewriting strategy. In this work, we propose to adapt the Tree Automata Completion algorithm to accurately approximate the set of terms reachable by rewriting under the innermost strategy. We prove that the proposed technique is sound and precise w.r.t. innermost rewriting. We also show that it noticeably improves the accuracy of static analysis for functional programming languages using the call-by-value evaluation strategy.