The sculpture sits atop a 13ft (4m) pole
Artist Tracey Emin could take her bronze sparrow away from Liverpool if anyone else "borrows" the sculpture.
The 4in (10cm) sparrow, which sits on a 13ft (4m) pole beside the oratory at the Anglican Cathedral, has been stolen twice in the last three months.
It has been returned on both occasions but the artist says she could consider its future in the city if the £60,000 work goes missing again.
She said the thieves were "biting the hands that feed" in their actions.
The bronze sparrow forms part of the artwork "The Roman Standard" which the BBC commissioned for the art05 festival three years ago.
Miss Emin is currently displaying a neon artwork inside the cathedral as part of an independent strand of the Liverpool Biennial arts festival.
Speaking about the sparrow, she told BBC Radio Merseyside: "It is so sweet. It's so harmless. It flew to Liverpool.
"Liverpool gave me the idea and people loved it and the fact some fool has decided to steal it... all you are doing is stealing from the place you live, biting the hand that feeds you.
"It really isn't worth it, otherwise you'll lose it completely - I'll take it away."
After its latest flight, the bird was handed to police who in turn passed it over to BBC Radio Merseyside on 13 September.
When the sculpture previously disappeared in July an anonymous caller telephoned the radio station a few days later to tell them where it had been deposited.
The message left at the BBC said it had been left in the grounds of The Oratory on Upper Duke Street and the bird was subsequently found in an envelope marked "FAO Tracey Emin: URGENT!"
A note inside read: "We are sorry - No harm meant. We would have returned it sooner but we were scared xxx."