The invitation would would break with royal precedent.
When the 92-year-old Monarch heard about it she told Doria she could come to Sandringham.
American social worker Doria was the only member of Meghan's family in attendance at her and Harry's wedding after Thomas Markle (74) was unable to walk his daughter down the aisle due to health reasons, The Sun reports.More news: Colorado man pleads guilty to killing pregnant wife, kids
Queen Elizabeth has asked members of the Middleton family to attend Christmas mass, but never to dine in Sandringham.
When the royal baby news was revealed in October, the grandmother-to-be was said to be "very happy about the lovely news" and looking forward "to welcoming her first grandchild", according to a statement from Kensington Palace.
Meghan and her mum, Doria Ragland, are said to have a close relationship. Instead, they have stayed at nearby Amner Hall rather than Sandringham, where the Queen resides during her trips to the country. 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! "They speak on the phone pretty much every day and they are talking about Doria getting a place in the U.K.so that she can spend part of the year over here".More news: [Exclusive]: Nokia 9 renders and 360-degree video
The invitation to Christmas dinner has also fuelled rumours that Doria Ragland may move to London, from her home in Los Angeles.
On Christmas Day, the family attends Christmas services at St. Mary Magdalene church, which are followed by a Christmas Day meal featuring a Norfolk turkey as the main attraction.More news: Red Sox left insane tip after World Series celebration in LA