This paper introduces the Biometrics Data Space framework, which is a secure ecosystem built on Data Spaces technology and it is designed to address the challenges of suspect identification during cross-border crime investigation. Apart from Data Spaces technology, the proposed framework innovates by leveraging also Privacy Enhancing Technologies (PETs) and blockchain to enable secure, trustworthy, and sovereign data exchange between Law Enforcement Agencies (LEAs) across borders. Specifically, it utilizes advanced PETs, including Large-Scale Biometric Data Indexing based on deep hashing techniques and Homomorphic Encryption to allow for suspect identification without disclosing sensitive information of personal biometric data. Thus, it enables LEAs to securely compare and exchange encrypted sensitive biometric data, including facial images, fingerprints and voiceprints, while maintaining data privacy and data sovereignty. LEAs define the usage rules for the biometic data they own and these rules are enforced to and respected by the other LEAs participating in the Biometrics Data Space. The proposed architecture is designed to be scalable, allowing the incorporation of additional biometric modalitiies and the easy expansion and integration with new participant LEAs.