The article features the role of the EU in the Greater Eurasian Partnership (GEP), a common geo-economic area in Eurasia proposed by Russian President Vladimir Putin at the St. Petersburg Economic Forum in 2016. The author assessed the prospect of cooperation between the EU, China, and the Russian Federation on a bilateral level, including the GEP concept. The author sees no premises for establishing Greater Eurasia at present: the interactions between China and the EU and between China and Russia as part of The Belt and Road Initiative (BRI) are independent of each other. If relations between the Russian Federation and the EU ever return to normalcy, the parties can begin a multilateral cooperation in the field of infrastructure construction in Eurasia, e.g., multimodal transportation systems, as well as in the investment sector, e.g., the Asian Infrastructure Investment Bank.