The Duchess of Cambridge's family has joined the royals at church on Christmas morning but they have stayed at nearby Anmer Hall rather than Sandringham itself.
The Queen's invitation would show respect and also acknowledge that Meghan, unlike Kate, has no other family in Britain, the source said.
A spokesperson for Buckingham Palace declined to comment today.
Doria won widespread praise for her dignity at the royal wedding following weeks of family drama surrounding Meghan's father, Thomas Markle.
Mr Markle pulled out because of health problems just days before she was due to walk down the aisle and admitted he had staged paparazzi pictures.
He later said he had apologised to both Harry and Meghan and denied staging the shots for money, insisting they were taken in a bid to 'change his image'.
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.
