The Queen has been asking dinner guests to give her "three good reasons" why Britain should stay in the EU, according to a biographer.
Royal author Robert Lacey says the monarch has been challenging her inner circle over the upcoming EU referendum.
While suggesting she was a Eurosceptic, Lacey said her remarks did not indicate she was in favour of Brexit but instead that she wanted to encourage debate on the topic.
The disclosure, in an article for the Daily Beast, comes a month after The Sun newspaper was rebuked by the IPSO press regulator for publishing a front-page story which claimed the Queen backed leaving the EU.
The story claimed the monarch had a "bust-up" with ex-deputy prime minister Nick Clegg in 2011 at Windsor Castle over Europe, suggesting it was "heading in the wrong direction".
Clegg called the story "nonsense" after its publication while Buckingham Palace complained about the article, stressing The Queen was always politically neutral. IPSO later criticised The Sun for its "Queen Backs Brexit" headline, describing it "significantly misleading".
Lacey said the Queen has been "promoting the debate on both sides," but added there had been moments when she expressed frustration over certain decisions taken in Europe.
"We know from another leaked royal conversation that the European Court of Human Rights has annoyed the Queen as much as many Britons," Lacey wrote. "She felt that the court's shielding of Abu Hamza, the extremist Muslim cleric whom the Home Office wished to deport in 2012, 'denigrated' Britain."
Lacey later said of his article, which makes the case for remaining in the EU, that at the beginning of the year he had believed the Queen may have backed Brexit.
"At the moment from what I hear she is very much prompting the debate on both sides," he told The Times. "I would not like to suggest now that Her Majesty is taking sides. There have been moments when Europe — particularly over the Abu Hamza episode — tended her to some frustration, like we all feel.
"From what I hear, from the moment the referendum was called she has been neutral. If she talks like this at dinner parties, it is a matter of prompting debate in a creative fashion.
"I have no doubt that the Queen is a Eurosceptic. But that is not automatically to say she is a Brexiteer. You can be a Eurosceptic and want to make a fresh start, or a Eurosceptic and want to stay in and change things for the better."
The Queen will not be casting a vote on Thursday, in keeping with her political neutrality.
Buckingham Palace said: "The Queen remains above politics, and is strictly neutral. She is firmly of the view that the referendum on the European Union is a matter for the people to decide."
Recent polls suggest the EU referendum is on a knife-edge, with the latest telephone opinion poll from Survation, of more than 1,000 people on 20 June, putting Remain on 45% (=) and Leave on 44% (+2), with 11% of respondents undecided.