Her unwillingness to offer an insight into her personal thoughts on the matter is said to have come as a disappointment to both the Queen and Duke of Edinburgh, it was reported.
Neither Buckingham Palace nor Downing Street would comment on the report.
A palace spokeswoman said: “By long-established convention we never disclose details of discussions between the Queen and her prime ministers. Nor would we comment on anonymously sourced conjecture of this kind.”
Behind the scenes however there was irritation at the report, with one source insisting it was not representative of Mrs May’s conversations with monarch during her two-day stay in Scotland.
The visit – an annual fixture for prime ministers – came just two months after Mrs May entered No 10 following the resignation of David Cameron in the wake of the Brexit vote.
It is not the first time reporting of the Queen’s supposed concerns about the EU have sparked controversy.
Earlier this year, former deputy prime minister Nick Clegg flatly denied a report in The Sun that the Queen had vented her frustration with Brussels at him during a private lunch at Windsor Castle.
The latest report follows the departure of the Queen and the Duke for Norfolk for the start of their Christmas holidays after apparently recovering enough from “heavy colds” to make the journey.
The royal couple travelled by helicopter from Buckingham Palace to the Queen’s private Sandringham estate after they were forced to delay their journey on Wednesday after falling ill.