Her Majesty, who has been suffering mobility problems, is no longer expected to interrupt her holiday when Tory voters elect Boris Johnson’s replacement for No10.
Plans are now under way for Mr Johnson to be joined by either Rishi Sunak or Liz Truss and travel to see the Queen on Tuesday, September 6.
It would be the first time in living memory the so-called kissing of the hands happens outside London or Windsor.
The current advice issued to the Queen is understood to be based on concerns about her comfort.
A final decision on whether she stays put will be announced publicly next week because the outgoing and incoming Prime Ministers need advance notice.
The plans have sparked fresh health concerns coming just weeks after she wowed partying Brits during her glorious four-day Platinum Jubilee party in June.
A source said: “The Queen has now been advised not to travel.
“But obviously no one tells the Queen what to do and ultimately it is her decision, and as we saw when she made a third appearance on the Buckingham Palace balcony at the Jubilee she likes surprises.
“There are some parts of her role that Prince Charles can do on her behalf but the Queen is adamant that she appoints the Prime Minister.
“It may not be the best choice to make the Queen travel 1,000 miles there and back for a 48-hour visit when the Prime Ministers can easily get to Balmoral instead.”
It is understood when the Queen arrived in Scotland last month for her ten-week holiday she had hoped to make the journey south when the PM is appointed.
Windsor Castle had been earmarked for the traditional constitutional ceremony.
Sources say it is incredibly rare for any monarch not to anoint a new Prime Minister at Buckingham Palace or Windsor Castle.
The Queen kissed hands with her first PM Winston Churchill in 1952 at Heathrow when she returned from Africa after her father King George VI died.
Every other PM since has travelled to Buckingham Palace.
But in 1908 after the sudden resignation of a sickly Sir Henry Campbell-Bannerman the ceremony was carried out in France.
His replacement Herbert Asquith was forced to travel to Biarritz where the Queen’s great-grandfather King Edward VII was on holiday at the time.
There are some parts of her role that Prince Charles can do on her behalf but the Queen is adamant that she appoints the Prime Minister.
Asquith was appointed after an audience in a private room in a hotel and remains the only PM to have taken office on foreign soil. The Queen has suffered “episodic mobility problems” for almost a year and spent a night in hospital last October.
She arrived in Scotland on July 22 and was pictured walking down the steps of her plane after landing at Aberdeen airport.
A public ceremony welcoming the Queen to Balmoral was instead held behind closed doors amid concerns for her comfort.
Members of her family have been by her side at the 50,000-acre estate this summer.