The death 10 days ago of the famous merino wether from Bendigo Station sparked a discussion about the fate of his remains.
Shrek's minder and owner John Perriam originally planned to have him cremated and the ashes scattered, but a flood of calls, cards and emails from wellwishers, wanting to know if Shrek could be preserved and placed on display, has changed his mind.
The story of how Shrek was discovered in 2004 after evading muster and shearing for six years captured the imagination of international media and generated much publicity for New Zealand.
It raised funds for Tarras School and the Cure Kids charity.
Mr Perriam and Cure Kids fundraising and business development director Josie Spillane have been talking to Te Papa about the possibility of Shrek's preserved remains being displayed at the national museum.
"I'm hoping Shrek's internal organs can be cremated and scattered and that his outer body can be preserved and go on display at Te Papa, so everyone can view him and visit him," Mr Perriam said yesterday.
Te Papa spokeswoman Roxan Mathys confirmed staff had been "working through the steps" on whether that was possible, but nothing had been decided yet.
A decision would be made next week.
Mrs Spillane said the publicity following Shrek's death was greater than when he was discovered.
"It's been humbling and we're almost reeling from it ...
"It's been an outpouring of support rather than of grief."
Television crews from Germany, Hong Kong and Australia, as well as media from throughout New Zealand, wanted to attend any memorial service.
"What we'd like is for that service to be a real celebration of Shrek's life, maybe held at his unveiling in Te Papa when he goes on display, if they agree to have him," she said.