In addition to the current measures Europe has imposed on Member States to fight crime, Europe is considering a EU central asset registry. In 2021 a European tender on the subject was opened (blog post).

In June this year a member of the European Parliament asked questions on this registry:

The potential EU central asset registry and its compatibility with existing EU law

8.6.2022 (…)
The Commission has previously shown interest in the proposal for an EU‑wide asset registry (including through feasibility study 2021 / S 136‑358265). In recent days, the proposal has returned to public debate, not least the idea of including it in the AML package. In my opinion, this would be a mistake and would potentially risk undermining the broad support for the fight against money laundering.

I would therefore like to ask the Commission the following questions:
1. Does it consider the proposal for an EU central asset registry to be compatible with the General Data Protection Regulation?
2. Does it believe that an EU central asset registry would be compatible with the Treaties?

Commissioner McGuinness answered as follows and mentions the tender in 2021:

Answer given by Ms McGuinness on behalf of the European Commission
1.8.2022

In response to a specific request from the European Parliament for a ‘Pilot Project — Feasibility Study for a European asset registry in the context of the fight against money laundering (AML) and tax evasion’ in the context of the EU budget for 2020 [1], the Commission issued a call for tender on 16 July 2021 and on 3 December 2021 the contract was awarded to a consortium composed of Centre for European Policy Studies, VVA Brussels and Infeurope SA. The study is still at an early stage.
The Commission is fully aware and mindful not only of the operational but also of the legal challenges such a possible EU asset registry would entail.
This is why the contractor has been specifically asked in the terms of reference to assess the feasibility of the project from all angles, including legal aspects, and in particular the provisions of the EU Treaties, the EU Charter of Fundamental Rights and the General Data Protection Regulation [2].
The terms of reference clearly highlight that any option for the design and functionality of a possible EU asset register needs to factor in the above and must include a necessity and subsidiarity assessment.
It should be noted that this study, undertaken at the request of the European Parliament and not included in the Anti-money laundering and countering the financing of terrorism legislative package proposed by the Commission in July 2021 [3], will by no means prejudge possible future policy initiatives of the Commission, which remain subject to Better Regulation principles.

[1] See Working document on Pilot projects and Preparatory actions in budget 2020 and 2021, https://www.europarl.europa.eu/doceo/document/BUDG-DT-648406_EN.pdf .
[2] Regulation (EU) 2016/679 of the European Parliament and of the Council of 27 April 2016 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing Directive 95/46/EC (General Data Protection Regulation) (Text with EEA relevance), OJ L 119, 4.5.2016, p. 1‐88
[3] https://ec.europa.eu/info/publications/210720-anti-money-laundering-countering-financing-terrorism_en