During the HBO series' sixth season, Davis's character Charlotte York received comfort after suffering a miscarriage by being given a Cavalier King Charles Spaniel called Elizabeth Taylor.
While appearing as a guest on Live with Regis and Kelly, the actress told Kelly Ripa and guest host Russell Brand that Taylor personally gave permission for her name to be used.
"Our writer Michael Patrick [King]… had gone to Elizabeth Taylor and asked her about the whole storyline, because remember it was the dog and Charlotte had a miscarriage and she's watching the life story of Elizabeth and that kind of gives her the gumption to get back up and face life and go on with her life," Davis said.
She added: "Elizabeth had been so sweet and she said, 'Of course', and she sent us all gifts, and she sent us a handwritten card... I just remember holding that card and thinking, 'Elizabeth Taylor wrote this to me!' It was just so generous and warm and wonderful and how you dream that all of those people are gonna be."
Davis further explained that receiving a personal note from the two-time Oscar winner was a truly heart-warming moment.
"When things like that happen - people that you've grown up watching - and they're so generous and kind of better than you would expect them to be, it's a wonderful thing," she added.
Christie's confirmed on Sunday that a selection of Taylor's jewels will be put on the auction block for a series of public sales.
> Obituary: Elizabeth Taylor
> Stars pay tribute to Elizabeth Taylor
> In Video: Elizabeth Taylor's movie roles
> In Pictures: Elizabeth Taylor on screen
> Elizabeth Taylor: A Life In Pictures
> Elizabeth Taylor: Her life on TV
> Elizabeth Taylor on Hollywood, sex and marriage