Most deep noise suppression (DNS) models are trained with reference-based losses requiring access to clean speech. However, sometimes an additive microphone model is insufficient for real-world applications. Accordingly, ways to use real training data in supervised learning for DNS models promise to reduce a potential training/inference mismatch. Employing real data for DNS training requires either generative approaches or a reference-free loss without access to the corresponding clean speech. In this work, we propose to employ an end-to-end non-intrusive deep neural network (DNN), named PESQ-DNN, to estimate perceptual evaluation of speech quality (PESQ) scores of enhanced real data. It provides a reference-free perceptual loss for employing real data during DNS training, maximizing the PESQ scores. Furthermore, we use an epoch-wise alternating training protocol, updating the DNS model on real data, followed by PESQ-DNN updating on synthetic data. The DNS model trained with the PESQ-DNN employing real data outperforms all reference methods employing only synthetic training data. On synthetic test data, our proposed method excels the Interspeech 2021 DNS Challenge baseline by a significant 0.32 PESQ points. Both on synthetic and real test data, the proposed method beats the baseline by 0.05 DNSMOS points - although PESQ-DNN optimizes for a different perceptual metric.