A court in Derry heard how the donkey would have to be euthanized after it was found wandering in a neglected state in Claudy.
A council solicitor told Derry Magistrates Court how the owner of the animal could not be found.
Deputy District Judge Brian Archer said the court would allow Derry and Strabane District Council to put the animal to sleep.
However, Danny Curran of the Donegal Donkey Sanctuary in Raphoe said he would not stand by and watch the donkey put down.
Danny and his team currently home more than 70 donkeys, many of whom have been abandoned and neglected.
Derry Magistrates Court now has 14 days to find the owner of the donkey which is under the supervision of vets at Derry and Strabane Council.
But Danny and his team have already been in touch with Derry and Strabane Council to organise a cross-border handover of the donkey if an owner cannot be found.
He said he also plans to name the donkey ‘Brexit’ in honour of the UK’s decision to leave the European Union.
“I think it’s nice that we can do this small thing for the UK before the leave the European Union. I was thinking of calling it Theresa Nay but that would be too cruel,” he laughed.
He added “On a more serious note, we are willing to take the donkey into our care. We will never stand by and watch a donkey put to sleep when we can step in and try to help it.
“Many of the donkeys who come to us are in a very neglected state but we manage to get them back to a god state of health to live out their days here with us in Raphoe.”