Palace officials told the BBC that Prince Harry, the Duke of Cambridge and the Prince of Wales would all attend, while Meghan is expected join the discussion over the phone from Canada.
The Sussexes say they plan to step back as senior members of the Royal Family.
There is no suggestion a conclusion will be reached at the meeting.
But BBC royal correspondent Jonny Dymond said it is hoped that the talks will produce a “next step” on the way to defining the couple’s new relationship with the Royal Family – in line with the Queen’s wish to find a solution within days.
He added that there were still “formidable obstacles” to overcome in the talks.
Meanwhile, the Duke of Cambridge has spoken of his “sadness” at the broken bond with his brother, the Sunday Times reports.
According to the paper, Prince William told a friend: “I’ve put my arm around my brother all our lives and I can’t do that any more; we’re separate entities.
“All we can do, and all I can do, is try and support them and hope that the time comes when we’re all singing from the same page.”
Monday’s gathering at the Queen’s estate in Norfolk – being described as the “Sandringham summit” – will be the first time the monarch has come face-to-face with Harry since the Sussexes’ announcement, which was posted on their official Instagram account.
BBC royal correspondent Nicholas Witchell said the trickiest area will be to agree the financial position of the Sussexes, who said in their statement on Wednesday they intend to “step back” as senior royals and work to become financially independent.
The couple also said they plan to split their time between the UK and North America, while “continuing to honour our duty to the Queen, the Commonwealth, and our patronages”.
There are likely to be tax implications to any decision to base themselves outside the UK for any length of time and Buckingham Palace will want “tight protocols to prevent them cashing in on their royal status”, our correspondent added.
The Royal Family was said to be “hurt” at the couple’s statement. It is understood the Queen was not consulted in advance of their decision.
The Queen, Prince Charles, William and Harry are expected to review a range of possibilities for the Sussexes, taking into account plans outlined by the couple.
If a deal is agreed in the coming days, there is a general understanding that it will take some time to implement.
Prince Charles is currently in Oman, after travelling overnight to attend the first of three days of official condolences alongside the Prime Minister Boris Johnson, following the death of Sultan Qaboos bin Said Al Said. He will return to the UK in time to attend Monday’s talks.
On Sunday morning the Queen was seen smiling and waving to crowds as she was driven to church in Sandringham.
Meanwhile, Meghan is in Canada with her eight-month-old son Archie after flying there amid the ongoing discussions, which have involved the UK and Canadian governments.
She and Prince Harry had been in Canada over Christmas, before they returned to the UK on Tuesday after a six-week break from royal duties.
On Friday, the couple’s official Instagram account returned to publicising their appearances.
Pictures were posted showing the couple during a private visit on Tuesday to a community kitchen in north Kensington, west London, where meals were cooked for families displaced by the Grenfell Tower fire.
Last October, Prince Harry and Meghan publicly revealed their struggles under the media spotlight.
Former actress Meghan, who is American, lived and worked in Toronto where she starred in the popular US drama Suits.
The couple were already preparing to launch their own Sussex Royal charity, which they set up after splitting from the Duke and Duchess of Cambridge’s foundation in June last year.
It was revealed in December the couple had made an application to trademark their Sussex Royal brand across a string of items including books, calendars, clothing, charitable fundraising, education and social care services.