This paper addresses the problem of scalability for a cell-free massive MIMO (CF-mMIMO) system performing Integrated Sensing and Communications (ISAC). Specifically, the case in which a large number of access points (APs) are deployed to perform simultaneous communication with mobile users and surveillance of the surrounding environment in the same time-frequency slot is considered, and a target-centric approach on top of the user-centric approach used for communication services is introduced. Consideration of other practical aspects such as the fronthaul load and scanning protocol issues are also treated in the paper. The proposed scalable ISAC-enabled system has lower levels of system complexity, permits to manage the case in which multiple targets are to be tracked/sensed, and achieves performance levels superior or in some cases close to those of the non-scalable solutions.