The Australian Broadcasting Corporation said the Thai mother of the children, Siriwan Nitichad, had agreed to carry a child for the man and his wife who had not been able to conceive.
"She said her husband wanted to have a baby so much, please help them, please help them," the woman, who is also known as Aon, told the broadcaster.
Aon, who lives in Phetchabun province north of Bangkok, said she agreed to use her own eggs, was paid about Aus$5,500 (US$5,122) and gave birth to twins some years ago. The report did not specify the age of the children.
The Australian couple took the children home, but court documents reveal that the father, who cannot be named, was last year charged with indecently dealing with them, the ABC said.
The man, who reportedly denies the allegations which also include the alleged possession of child abuse material, is expected to fight the charges when they come before court later this year.
The children have remained with the man's ex-wife but Aon said she was open to the idea of taking the twins back.
"If they don't have anyone to take care of them, we are happy to take care of them," she said.
The case follows that of baby Gammy who was born with Down's syndrome to a Thai surrogate for an Australian couple in December.
In that case, which sparked global debate, the couple took the boy's healthy twin sister back to Australia but left Gammy in Thailand.
It prompted calls for tighter controls by authorities in Bangkok and raised concerns about the practice of international surrogacy, particularly after it emerged that the father had previously been convicted of child sex charges.
That couple have denied deliberately abandoning their baby son and have said they will try to get him back.
Commercial surrogacy is illegal in Australia, but growing numbers of people are travelling to countries such as India and Thailand to engage women to carry their babies.
Surrogacy Australia, a non-profit agency which assists couples engaging in surrogacy, said the latest case was about child abuse, not how the children were conceived.
Executive officer Rachel Kunde said any child could be at risk of abuse by their parent and whether they were born through surrogacy was not the issue.
She said she would support a move to ensure all people undergoing surrogacy were screened for their criminal background.
"However it is not clear whether the father in this case had a criminal history so it may not always be beneficial," she said.