The Queen has been canvassing opinion on the EU debate by asking dinner companions: "Give me three good reasons why Britain should be part of Europe."
Her Majesty's biographer, Robert Lacey, reported the Queen's comments and suggested they may mean the Queen favours withdrawal from the European Union.
Buckingham Palace would neither confirm nor deny that the Queen had been debating the merits of Brexit in private, but royal sources pointed out that the words attributed to the Queen were "a question, not a statement".
However, the leading nature of the alleged question adds weight to previous claims that the Queen would like Britain to pull out of the EU.
Last month the press regulator found that the Sun newspaper had been guilty of "significantly misleading" its readers when it printed the headline "Queen backs Brexit" above a story about the Queen complaining about Brussels to Nick Clegg.
One royal insider said of the latest report: "She appears to be asking a question, not making a statement.
She is not expressing a view."
The Queen is, officially at least, politically neutral, but she intervened in the Scottish referendum debate in 2014 by suggesting in a conversation with a member of the public, which she knew was likely to be reported by the press, that she hoped Scots would "think very carefully" before casting their vote.
It was seen as a clear indication that the Queen wanted Scotland to remain part of the United Kingdom.
Lacey made his claim about the Queen questioning dinner guests in a blog for the Daily Beast website.
He told the Telegraph: "She asked the question in the context of a general debate - she loves a bit of forthright discussion and this sort of remark is tossed around the dinner table like a ping pong ball. That is the way she frames her questions."
A spokesman for the Queen said: "We would not comment on private conversations the Queen may or may not have had."