Palace officials told the BBC that Prince Harry, the Duke of Cambridge and the Prince of Wales will 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.
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.
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.
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.