The move is somewhat unprecedented, as a member outside of the Royal family has not been invited to stay at the Norfolk estate during the Christmas period before.
The Queen's invitation would show respect and also acknowledge that Meghan, unlike Kate, has no other family in Britain, the source said.
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The House Of Windsor have previously arranged for the Duchess Of Cambridge's family to join them at church on Christmas morning but they did not stay at Sandringham.
A spokesperson for Buckingham Palace declined to comment.
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Meghan Markle rocked an electric blue ensemble from her wedding dress designer Givenchy - but what most style spotters failed to notice was that the fabulous pleated skirt that she combined with the matching sweater was see-through!
"Doria's quiet dignity and grace at the Royal wedding has earned her enormous respect from Meghan's new in-laws", the source tells ET.
Mr Markle was due to walk his daughter down the aisle but pulled out at the last minute after it emerged he had staged paparazzi pictures in the days prior to it.
The invitation is fuelling speculation that Doria - who is now based in Los Angeles - may remain in London for the duration of Meghan's first pregnancy.
Doria was also in London in September and joined her daughter at an outdoor reception at Kensington Palace to mark the launch of a cookbook.