The Heng Yuan Xiang group had contacted the New Zealand Wool Testing Authority and expressed interest in buying Shrek's remains.
"They asked to buy the carcass and we said no. Then they asked to buy the fleece and we said no again. They then said they would pay $1000 for a staple," Mrs Spillane said.
A staple was a small amount of his wool, she said.
"Originally, 500 were produced and we still have a couple left. We auctioned them off starting at $100 and the first one sold for $5000, but most went for between $100 and $200."
Shrek's owner, John Perriam, is in China at present.
"We are looking at getting John to hand over the staple. If he does, then the group will pay $5000 for it," Mrs Spillane said.
The money would go to Cure Kids.
Mrs Spillane said she was meeting Te Papa representatives today and "it is looking really positive that Shrek will go to Te Papa".
She said David Jacobs, the taxidermist, will soon take Shrek's death mask, an impression of the famous sheep's face, so he can make a lifelike face when Shrek is mounted.
They won't know if Shrek can be preserved for another couple of weeks, "probably the end of July", Mrs Spillane said.