The pair, who divorced in 1996, both reside at the Royal Lodge on the Windsor estate.
The source told CNN that the Duchess bonded with the monarch over a shared love of dog-walking and horse-riding.
Even after her divorce from Prince Andrew, Sarah continued her friendship with the Queen by walking dogs through the Windsor estate, the source added.
She is also reported to have left behind an older, mixed breed “dorgi” called Candy and a cocker spaniel named Lissy. It is unclear who will be looking after Candy and Lissy.
Corgis have become synonymous with the monarch, who throughout her long life was regularly photographed with a Welsh corgi at her feet.
The Queen was often credited with creating the dorgi breed when her corgi mated with a dachshund owned by her sister, Princess Margaret.
The Queen’s passion for corgis dated back to her childhood, when she fell in love with her father King George VI’s dog, Dookie. In 1944, on her 18th birthday, she was given a Pembroke Welsh corgi puppy named Susan. Such was her attachment to Susan, she reportedly took her on her honeymoon in 1947. Susan died in January 1959.
The monarch went on to own dozens of corgis in her lifetime. One, Willow, famously appeared alongside her in the James Bond sketch that she recorded for the opening ceremony of the 2012 London Olympics.
The prince has repeatedly denied wrongdoing. Still, the allegations against Andrew, 62, have dramatically tarnished his public standing.