The Sun quotes anonymous sources, one of whom claims to have witnessed a "bust-up" between the Queen and pro-EU former Deputy PM Nick Clegg in 2011.
It says the Queen told Mr Clegg the EU was "heading in the wrong direction".
Buckingham Palace said it would not comment on "spurious" claims, and Mr Clegg called the story "nonsense".
Under the headline "Queen backs Brexit", the Sun says the Queen's exchange with Mr Clegg at a lunch in 2011 left "no room for doubt about her passionate feelings over Europe".
It says her "reprimand" of Mr Clegg "went on for some time and stunned other guests".
The paper says the Queen also revealed her feelings about Europe during a separate conversation with MPs at Buckingham Palace "a few years ago".
It claims the Queen told them: "I don't understand Europe" - words an unnamed parliamentary source says she spoke with "venom and emotion".