Deborah Hubbard's cockatiel Ziggy flew off when a neighbour unwittingly walked outside with him on her shoulder.
Ziggy, who is pale grey with a yellow head, went missing from Longden Coleham in Shrewsbury last Tuesday, March 1.
"I'm absolutely heartbroken," said Deborah. "I'm really hoping he's landed on someone's bird feeder and someone out there is looking after him. That's really my only hope.
"He is such a character. Everyone loves him. I just hope we can get him back."
As well as the Addams Family theme tune, Ziggy also responds to Pop Goes The Weasel and September, by Earth, Wind and Fire. "He's got a few sayings as well," added Deborah. "He says 'who's a pretty boy' and 'you've been a good boy'."
A few sightings in the Belle Vue area of Shrewsbury have been reported, but sadly they were false dawns. "I've had a few calls that there's a wild parrot in the area," Deborah added. "But I'd rather people get in touch and it be a wrong sighting rather than people don't phone up.
"I'm prepared to do anything to get him back," she added.
Have you seen Ziggy? If so, call Deborah on 07891 615406.