The US-China Economic and Security Review Commission’s 2018 Annual Report to the US Congress deals, among other issues, with China’s influence. Ivana Karásková, ChinfluenCE lead coordinator, and Matej Šimalčík, project’s coordinator for Slovakia, were interviewed for the report. They argue that the current EU investment screening mechanism addresses media investments, but the measure is not robust enough because it creates only a reporting procedure, not a regulatory framework. On the member states level, it would be wise to consider media as a strategic industry (in political, rather than economic sense) and protect them through the screening mechanism or at least, for instance, law prohibiting cross-media ownership. Such a law already exists in Slovakia.
The full report could be found here. The media ownership is addressed at Chapter 3, Section 2.