The actress-and-model is besotted with her Blue Fronted Amazonian, who she has named Ping Pong, and is trying to get her pet to serenade her.
Speaking to her rumoured boyfriend, Australian cricketer Shane Warne, she wrote on her twitter page: "@warne888 Trying to teach her to sing Rule Britannia-maybe I`ll attempt Waltzing Matilda too so she can serenade you- (sic)"
Hurley has also been trying to teach Ping Pong to speak and today (27.01.11) her feathered friend finally uttered her first unexpected words.
She tweeted: "Ping Pong just mumbled her first words! High excitement. She has a very deep, alarmingly manly voice."
It seems the sportsman is getting jealous of all the attention the 45-year-old brunette is lavishing on her bird and instead wants Elizabeth to leave the parrot on her perch and go to Australia to see him.
Writing to Elizabeth, he tweeted: "I`m getting jealous of ping pong! Think it`s time you left ping pong alone for a while & come visit me in Australia. (sic)"
However, the `Austin Powers-` star was quick to reassure the 41-year-old sportsman Ping Pong hasn`t taken his place in her affections.
She wrote on the micro-blogging site: "@warne888 No need for jealousy SW, she`s not getting any cuddles or kisses! (sic)"