Fenick, who was considered to be the country's leading expert on mole-catching, began working for the Queen at Sandringham more than 30-years ago.
As a result Her Majesty got to know his wife, Nancy very well and the pair became close friends.
In the 1980s Mrs Fenwick agreed to take on the role of training and looking after the royal dogs.
Mrs Fenwick was trusted to care for them while the Queen was overseas on official visits and knew all of their dietary needs and particular likes and dislikes.
Over the years the Queen built up a close bond with the Fenwicks and as a gesture of appreciation for their support, even gifted them one of the corgis, she had bred.
When Mrs Fenwick died in 2015, aged 85, the Queen even attended her funeral.
Fenwick's death last week has now left the Queen considering whether to take on the his corgi and Bichon Frise if there is nobody in his family who is able to do so.
A royal insider said: "The Queen was very fond of Nancy and Bill and they became close friends."
The source added: "Bill was not in the best of health and was unable to exercise the dogs much. So most Sundays after lunch the Queen would visit him and take the pair out in the park."
The source went on: "She was very upset to hear about Bill's death and she is considering taking the dogs if his family can't look after them."
The Queen currently has one corgi, called Willow as well as two corgi-dachshund crosses, Vulcan and Candy.
One of her favourite dogs, Holly, who starred alongside her in the famous London Olympics, James Bond sketch, had to be put down several months ago due to illness and old age.
The Queen's passion for corgis goes back to her childhood and she began breeding after being given a dog called Susan for her 18th birthday in 1944.
She has owned more than 30 dogs during her lifetime and at one stage had 13.
But three years ago she decided not to breed anymore amid fears that she and the Duke of Edinburgh could suffer a fall if they had boisterous puppies around their feet.
Sources have also suggested that the Queen was reluctant to have any of her pets left behind when she passes away.