6G wireless networks are expected to provide seamless and data-based connections that cover space-air-ground and underwater networks. As a core partition of future 6G networks, Space-Air-Ground Integrated Networks (SAGIN) have been envisioned to provide countless real-time intelligent applications. To realize this, promoting AI techniques into SAGIN is an inevitable trend. Due to the distributed and heterogeneous architecture of SAGIN, federated learning (FL) and then quantum FL are emerging AI model training techniques for enabling future privacy-enhanced and computation-efficient SAGINs. In this work, we explore the vision of using FL/QFL in SAGINs. We present a few representative applications enabled by the integration of FL and QFL in SAGINs. A case study of QFL over UAV networks is also given, showing the merit of quantum-enabled training approach over the conventional FL benchmark. Research challenges along with standardization for QFL adoption in future SAGINs are also highlighted.