But because Ali Nesha was not included, they declined, determined to stay together.
"My brother said, '[If] my grandmother [isn't] going, my family [is] not going to America'," one of Ali Nesha's granddaughters, Tara Begum, told the Sydney Morning Herald.
Last year, the family resolved to take their fate into their own hands. Clubbing together, they acquired a boat - and, armed only with a map, their UNHCR passports and the clothes they wore - set off for Australia or New Zealand.
Unlike most boat people, they did not pay a "people smuggler". They had no trained crew and no GPS equipment.
On board was every member of the family, except for a son-in-law of Ali Nesha's, who is asthmatic and feared he might not survive the journey, two of his daughters and their husbands, who stayed in Malaysia.
The old lady coped well with the 10 days at sea, mostly sleeping.
"She is very special," said Tara Begum, adding that everyone else was seasick and frightened.
Now in community detention in Melbourne, Ali Nesha hopes that some of her Brisbane friends will visit her on her 100th birthday.