Groups of around 19 athletes staying at the village or with families in south-east Queensland made a run for it during the Gold Coast event.
The Refugee Advice and Casework Service (RACS) group in Sydney said it had received enquiries from several of them but declined to reveal the exact number or the countries of origin.
The 11 athletes disappeared from the Gold Coast at various times over the course of the games.
Athletes from Cameroon enter the stadium for the Opening Ceremony. Policy would dictate that a bridging visa should be issued while a protection claim was assessed, she said.
"The compliance officers will be out there, I promise, tracking these people down and they will be deported as quickly as possible", he said. "Often the delay is an inability to get legal advice".
"The men, women and families who are recognised as needing protection in Australia are allowed to remain only after a complex and hard process".
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"The process can take many months, sometimes it takes years. With none of this work funded by government in 2018, we rely on our volunteers, partners and supporters to make sure people who seek asylum have an opportunity to live a life in safety".
Rogue athletes aren't uncommon at big global sporting events, and Australia saw similar circumstances after the Sydney Olympics in 2000.
The visa is said to be expiring on Tuesday, after which, if found, they will be detained and deported unless they have applications for another in progress.
They arrived in Sydney less than 24 hours before their visas expired to leave Australia, or risk detention or deportation.
Cameroon weightlifter Olivier Matam was one of the athletes who went missing. Of those, 14 from Sierra Leone were granted asylum and eventually settled in Sydney.
"If they breach the conditions, they're subject to enforcement action", Dutton told reporters on Tuesday.