The invite could mean Harry and Meghan will stay with her briefly when other senior royals are not around.
The couple left the UK in 2020 and have not visited the Highlands since 2018. They returned to Britain in June for the Queen's Platinum Jubilee but remained in the background for most of the festivities.
Another source said Balmoral was the "perfect place" for them to spend some quality time with the Queen.
"They barely had 15 minutes with her at the jubilee."
But another source told The Sun, "I would be stunned if they did turn up."
The Sussexes, whose relationship with the senior royals is under strain, secretly visited the Queen and Prince Charles on their way to the Netherlands for the Invictus Games in April.
They introduced baby Lilibet to the Queen during the Jubilee.
A new $35,000 wheelchair-friendly lift has been installed at Craigowan Lodge for the Queen.
The monarch likes to spend her Scotland breaks surrounded by family members visiting in turns. William and Kate brought their children last year, while Edward and Sophie also visited with theirs.
The disgraced Prince Andrew hid on the estate for weeks while American lawyers attempted to serve his sex abuse writ.
In the past, the Queen and Prince Philip would host family barbecues at the lodge.
Her granddaughter Princess Eugenie has said it's "the most beautiful place on earth".
"I think Granny is the most happy there."