Source-Free Domain Adaptive Object Detection (SF-DAOD) aims to adapt a detector trained on a labeled source domain to an unlabeled target domain without retaining any source data. Despite recent progress, most popular approaches focus on tuning pseudo-label thresholds or refining the teacher-student framework, while overlooking object-level structural cues within cross-domain data. In this work, we present CGSA, the first framework that brings Object-Centric Learning (OCL) into SF-DAOD by integrating slot-aware adaptation into the DETR-based detector. Specifically, our approach integrates a Hierarchical Slot Awareness (HSA) module into the detector to progressively disentangle images into slot representations that act as visual priors. These slots are then guided toward class semantics via a Class-Guided Slot Contrast (CGSC) module, maintaining semantic consistency and prompting domain-invariant adaptation. Extensive experiments on multiple cross-domain datasets demonstrate that our approach outperforms previous SF-DAOD methods, with theoretical derivations and experimental analysis further demonstrating the effectiveness of the proposed components and the framework, thereby indicating the promise of object-centric design in privacy-sensitive adaptation scenarios. Code is released at https://github.com/Michael-McQueen/CGSA.