She said Pinnawala identified captive-born Nandi - "who is the right age and maturity to be re-homed" - as the ideal candidate.
"Auckland Zoo experts have also assessed Nandi, and consider her to be of the right temperament to be a great companion for Anjalee and Burma."
But the spokeswoman said there is still a long road ahead before the new baby elephant can arrive in New Zealand.
"It is exciting for us - but there is still a lot more to do before it is 100 per cent confirmed Nandi will be flying our way."
Like Anjalee, she will have to go through routine testing over the next few months before being able to settle into her new home.
Sri Lanka's president Maithripala Sirisena presented a deed of ownership for Nandi during a red-carpet welcome on Wednesday in Colombo for Prime Minister John Key, who arrived for a two-day official visit.
But the gift sparked anger from animal rights activists who said it was cruel to separate the young elephant from her family.
The Auckland Zoo spokeswoman said the Sri Lankan elephant orphanage was currently home to 93 elephants, all of which are unable to be released into the wild.
She said Pinnawala, which was originally built to house 30 elephants, regularly re-homes elephants of Nandi's age to other facilities.
"Regarding the welfare concerns raised in Sri Lanka, we're confident we can provide Nandi with a great life as we have and continue to with Anjalee," she said.
Sri Lanka has a long history of giving elephants as presents. It has given three to China and two each to Japan, South Korea, the Czech Republic and the United States.
Activists have urged the Sri Lankan government to halt the practice, saying some of the animals had found it difficult to adapt to their new climates and without their families.
"We are very disappointed," Sagarika Rajakarunanayake, head of the Sathva Mithra (Friends of Animals) group, told AFP.
"We wrote three weeks ago asking the government to stop this practice. I think they don't even read our letters."
Environmental lawyer Jagath Gunawardana said the government had given away too many, describing the animals as sacred in the mainly Buddhist nation.
"There should be a stop to these knee-jerk gifts of baby elephants," Gunawardana said.
The Sri Lankan government said the elephant was given in recognition of "excellent bilateral relations" with New Zealand.
Auckland Zoo director Jonathan Wilcken said elephants are extraordinarily powerful ambassadors for wildlife and the natural world and that this was one of the many reasons zoo staff are very excited about Nandi joining Anjalee and Burma.
She would become part of Auckland Zoo's sustainable breeding herd, he said.
"For many years, Auckland Zoo has also contributed significantly to programmes in Sri Lanka aimed at helping protect and conserve these extraordinary animals in the wild, where they remain threatened."
Since arriving in Auckland last June, Anjalee has put on 700kg and has developed a strong relationship with Burma.
- additional reporting by AFP
