According to the newspaper, the duo who have already had their visas revoked, are Sudanese-born Isaac Gatkuoth, 19, and a New Zealand-born member of the gang, 20.
Apex - which takes its name from a street in Dandenong, Melbourne, has recently gained notoriety for violence, thefts and carjackings.
Gatkuoth has denied being part of the gang.
Immigration Minister Peter Dutton refused to comment about the pair to the Herald Sun.
However, he said he was still focused on revoking the visas of criminals.
In April, the Australian Government revoked the visa of an associate of the Apex gang, who was deported to New Zealand.
"Australia is a generous nation and we settle a record number of people in our country each year, but we won't hesitate to cancel visas of people who commit crimes against Australians."
Previously, members of outlaw motorcycle gangs have felt the effect of the 2014 law change.
Since that came into effect, more than 1500 people have had their visas cancelled.