We introduce an inexact IRKA framework for $\mathcal{H}_{2}$-optimal model reduction of large-scale linear time-invariant SISO systems. In this approach, the costly direct solutions of shifted linear systems are replaced by fast, error-controlled reduced basis approximations. Reduced bases are constructed using two complementary strategies: a POD-based method and an error-driven Greedy-Galerkin method. The resulting reduced solutions are employed to compute the projection matrices for arbitrary shift parameters within the IRKA iterations.