Regression testing is key in verifying that software works correctly after changes. However, running the entire regression test suite can be impractical and expensive, especially for large-scale sys tems. Test suite optimization methods are highly effective but often become infeasible due to their high computational demands. In pre vious work, Trovato et al. proposed SelectQA, an approach based onquantumannealing that outperforms the traditional state-of-the art methods, i.e., Additional Greedy and DIV-GA, in efficiency. This work envisions the usage of Quantum Approximate Opti mization Algorithms (QAOAs) for test case selection by proposing QAOA-TCS.QAOAsmergethepotentialofgate-basedquantumma chines with the optimization capabilities of the adiabatic evolution. To prove the effectiveness of QAOAs for test case selection, we pre liminarily investigate QAOA-TCS leveraging an ideal environment simulation before evaluating it on real quantum machines. Our re sults show that QAOAs perform better than the baseline algorithms in effectiveness while being comparable to SelectQA in terms of effi ciency. These results encourage us to continue our experimentation with noisy environment simulations and real quantum machines.