She also assured Harry that they still had a place in the family but with reduced ownership.
This came in response to Harry and Meghan's announcement of their decision to separate from the royal family, and to start together an independent life in Canada.
The sources say: The Queen and Prince Charles are not ready to leave Meghan and Harry despite the damage to the family.
Senior aides Buckingham Palace, Clarence House and Kensington Palace have emerged from meetings and conferences increasingly optimistic that all parties can reach an agreement.
Ministers and officials from the United Kingdom and Canadian governments have been consulted, which may have to spend millions to support Sussex.
A royal source said: Prince Harry wishes to reach a solution, as well as all those in the palace, and that the solution satisfies all parties.
These talks were held after Megan returned to her home in Canada on the island of Colombia.