Mohammed and Abdullah Ayub were arrested in a CIA sting last month along with a third Australian, Polish-born Marat Sumolsky, 35, who lives overseas, according to reports in News Limited newspapers.
The three are among a group of eight foreigners with suspected links to al-Qaeda who are facing terrorism charges in Yemen over an alleged plot to smuggle arms to Somalia.
The Ayub boys were being watched because their father, Abdul Rahim Ayub, and his twin brother, Abdul Rahman Ayub, were believed to be the Jemaah Islamiah agents who set up a Sydney cell called Mantiqi4, in the lead up to the 2000 Olympics.
Their Australian-born mother, who reportedly swapped hippie beads for a burqa in Indonesia, heads a radical Islamic wives club whose husbands were arrested over the Kings Cross plot, the newspapers say.
Rabiah Hutchinson is in Yemen with her jailed sons, aged 18 and 20.
The Ayub's Sydney lawyer, Adam Houda, says his clients have done nothing wrong.
Australian consular officials are expected to be granted access to the trio today.