Authorities this week ordered the little figure's removal after the artists included it without clearance.
But in a letter to Arts and Culture Minister Paul Mashatile, animal rights organisation PETA (People for the Ethical Treatment of Animals) asked to take in the orphaned animal.
It would "highlight the plight of the billions of rabbits and other wonderful animals who are slaughtered for their skins, used in forced labour, and kept in chains," the group said in the letter, forwarded to media.
The saga drew banter from some, who started a campaign called #savetherabbit on twitter. One joker also started an account on the microblogging site with the handle @mandelarabbit.
Also Read
Built at a cost of eight million rand (about $740,000), the 4.5-tonne sculpture is the largest of Mandela statues erected around the world.
It was unveiled just a day after Mandela was buried.
"We would be honoured to use the bronze rabbit... To honour Mandela's vision of a more peaceful, kinder world," said PETA.