In its report, Brugel argues that a "growing proportion" of inward investment in the EU's 27 member states comes from non-European SWFs and equivalent bodies with political regimes that are often "non-democratic".
While this could create political tensions, it could also present a "genuine security risk" in some cases, the thinktank said.
In order to address this risk without erecting unnecessary barriers to much-needed inward investment, the EU-level policy framework should be administered at state level, allowing countries to credibly address security risks and allowing for the exchange of best practice across the union, Brugel added.
Brugel's paper comes after the International Monetary Fund agreed a voluntary code of conduct with 26 SWFs covering issues such as governance and transparency.
The code was developed in response to Western concerns that the current economic crisis could lead to strategic assets such as energy firms or defence companies being purchased by potentially hostile SWFs.