She reportedly said she was "head over heels" with pride as Meghan helped prepare lunch for guests.
A source adds, "It's a mark of the Queen's respect for Meghan and an acknowledgment that she doesn't have any other relations in this country - unlike Kate, who has the support of a very close family".
The invitation would would break with royal precedent. The Queen usually spends Christmas and New Year's at her Sandringham estate, with members of her family often joining her.
A source told the Sunday Express that the invitation was a "very thoughtful gesture" and would both show respect and acknowledge the fact that Markle does not have any family in Britain.More news: Girl Scouts killed by truck while picking up trash in Wisconsin
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.
She attended the royal wedding alone after Thomas was forced to pull out due to health issues, and has since been welcomed into the royal family's inner circle by Prince Charles, who walked his future daughter-in-law up the aisle. But it turns out Meghan actually has a pretty adorable and unexpected relationship with her stepmother-in-law, the Duchess of Cornwall.
The 11-a-side game is played at Castle Rising, near Sandringham, and the princes normally play on opposing teams - with Kate's brother James Middleton previously joining too.
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.