The Queen is reported to have asked dinner guests to give her “three good reasons why Britain should be part of Europe”, according to royal author Robert Lacey.
Mr Lacey, writing for The Daily Beast website, said the monarch posed the challenge recently.
“'Give me three good reasons', she has apparently been asking her dinner companions recently, 'why Britain should be part of Europe?'” Mr Lacey wrote.
A Buckingham Palace spokesman said: “The Queen is above politics and acts on the advice of her Government in political matters.
“The referendum is a matter for the British people to decide.”
Mr Lacey told the Press Association: “The Queen likes a healthy debate around the dinner table. It was just a question.
“She's aware of the complexities for different parts of the UK.
“As we know, she's very careful not to betray whatever her personal opinions may be on this. You can say the same of her husband.”
The Queen's grandson Prince Harry broached the subject of the EU referendum at the street party for the monarch's official 90th birthday.
He brought up the debate over Brexit with dairy farmer Mike King, 46, and his wife Rachel, 48, from Iron Acton, near Bristol, as he chatted to them on The Mall.
But the Prince kept his own views close to his chest. Mr King said afterwards: “I told Harry we were farmers and were hardy so we're just used to the wet (weather).
“When he heard we were farmers, he said 'In or Out?' and I said I was going to ask him the same.
“I said 'I'm undecided', and he said: 'I'm not allowed to say'.”
Traditionally, the Queen and her family never vote or stand for election.
Although the law does not ban royalty from voting, it is considered unconstitutional for them to do so.
What has the EU ever done for us?
What has the EU ever done for us?
1/7 1. It gives you freedom to live, work and retire anywhere in Europe
As a member of the EU, UK citizens benefit from freedom of movement across the continent. Considered one of the so-called four pillars of the European Union, this freedom allows all EU citizens to live, work and travel in other member states.
2/7 2. It sustains millions of jobs
A report by the Centre for Economics and Business Research, released in October 2015, suggested 3.1 million British jobs were linked to the UK’s exports to the EU.
3/7 3. Your holiday is much easier - and safer
Freedom to travel is one of the most exercised benefits of EU membership, with Britons having made 31 million visits to the EU in 2014 alone. But a lot of the benefits of being an EU citizen are either taken for granted or go unnoticed.
4/7 4. It means you're less likely to get ripped off
Consumer protection is a key benefit of the EU’s single market, and ensures members of the British public receive equal consumer rights when shopping anywhere in Europe.
5/7 5. It offers greater protection from terrorists, paedophiles, people traffickers and cyber-crime
Another example of a lesser-known advantage of EU membership is the benefit of cross-country coordination and cooperation in the fight against crime.
6/7 6. Our businesses depend on it
According to 71% of all members of the Confederation of British Influence (CBI), and 67 per cent of small and medium-sized enterprises (SMEs), the EU has had an overall positive impact on their business.
7/7 7. We have greater influence
Robin Niblett, Director of think-tank Chatham House, stated in a report published last year: “For a mid-sized country like the UK, which will never again be economically dominant either globally or regionally, and whose diplomatic and military resources are declining in relative terms, being a major player in a strong regional institution can offer a critical lever for international influence.
Last month, the press watchdog ruled that The Sun newspaper had breached press regulations with its front page headline suggesting the Queen was in favour of the UK leaving the EU.
The headline, “Queen backs Brexit”, published in March, was “significantly misleading”, the Independent Press Standards Organisation (Ipso) said.
Buckingham Palace complained, insisting the Queen was “politically neutral”.
Ahead of the Scottish independence referendum in September 2014, the Queen told a well-wisher in the crowd after morning church at Crathie Kirk, near Balmoral, a few days before the vote: “Well, I hope people will think very carefully about the future.”
When Scotland voted no, Prime Minister David Cameron confirmed the Queen's delight at the decision when he was caught on camera saying: “She purred down the line.”
The EU referendum debate has so far been characterised by bias, distortion and exaggeration. So until 23 June we we’re running a series of question and answer features that explain the most important issues in a detailed, dispassionate way to help inform your decision.Reuse content