The twin's surrogate mother Pattaramon Chanbua, 21, claims that David and Wendy Farnell deliberately abandoned Gammy after learning he had Down's Syndrome, but the couple deny this.
It later emerged that David has a criminal record of child sex offences.
Australian child protection officers have now made contact with the couple following days of speculation about their whereabouts.
West Australian Child Protection Minister Helen Morton told 6PR Radio: "We've had telephone contact with the family and we're in the process of putting other arrangements in place."
She urged the public to give the family 'privacy and confidentiality' while the situation is assessed - a process which she said could take several weeks.
"This family needs the opportunity to have the considerations around the safety and well being of that child undertaken in a really private comfortable environment for them," she said.
Asked if she has any concerns about whether Gammy's twin sister was safe and in good care, she said that the department had no 'major' concerns at present, but would be considering how to ensure the safety of the baby.
"The options would include everything from putting a really well developed safety plan around the child if necessary in the home situation, or it could range right up to anything to do with the child living away from the home," she added.
More on Parentdish: Young adults with Down's Syndrome reassure expectant parents in moving video
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