And EU is being described as just as "anti-Russian" as NATO to be honest - it's EU that introduced sanctions on Russia, not NATO.
It's EU that disciplined Gazprom and disciplines member states to reduce their dependency on Gazprom.
So on all accounts you could say EU is a threat to the existing status quo in the relations between Russia and individual member states.
Except It's obviously no "threat" if Russia just wants to make business on fair grounds.