The 'Sun', Britain's most-read newspaper, quoted highly- placed anonymous sources as part of its front-page article headlined 'Queen Backs Brexit', alongwith a photograph of the 89-year-old monarch.
"The Queen remains politically neutral, as she has for 63 years. We would never comment on spurious, anonymously-sourced claims. The referendum will be a matter for the British people,"a Buckingham Palace spokesperon said.
Britain is to vote in a referendum on June 23 to decide if the country will remain in the EU or leave the 28-nation economic bloc.
The newspaper claims a "bust-up" between the Queen and pro-EU former UK Deputy Prime Minister Nick Clegg in 2011 in which the monarch told Clegg the EU was "heading in the wrong direction".
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Clegg has since dismissed the report as "nonsense".
"This is categorically untrue. Nick has no recollection of this conversation and it is not the sort of conversation you forget," a spokesperson for the former deputy PM said.
The paper also refers to a separate conversation with British lawmakers at the Palace a few years ago when it claims the Queen said: "I don't understand Europe".
These words, an unnamed parliamentary source said, she spoke with "venom and emotion".
Tom Newton Dunn, the 'Sun's' political editor, says that the paper would not have reported the Queen's remarks "had they not come from two different and impeccably placed sources".
Opinion polls show voters are divided over the UK's membership of the EU with both "Leave" and "Remain" camps intensifying their campaigns to garner votes.