The delegates are staying in crisis accommodation, saying they are fleeing persecution at home.
One of the delegates from Tanzania, who did not want to be identified, said he had received death threats for his work with people with HIV and albino children in his homeland.
Albinos in Tanzania have been known to be killed in murders linked to witchcraft.
The delegate said he nearly died in March after being chased by several people as he drove home from watching a soccer match.
"Those people they saw me and then they started chasing me, it was around 8pm in the evening," he said.
"So I got a very bad accident ... almost like dying. They wanted to kill me. After that crash, they disappeared completely because so many people came to give me help."
He said he planned to formally lodge his application for asylum later this month.
"I don't have faith [in] my own state government to protect me against these people," he said.
"I learn that Australia has a human rights reputation, that's why I seek protection here."
Delegates seek advice from refugee advocates
A spokesperson for Immigration Minister Scott Morrison said the Government would not discuss individual applications.
"All claims for protection are considered on their individual merits and according to law," the spokesperson said in a statement.
Pamela Curr, from the Asylum Seeker Resource Centre (ASRC) said the group whose visas had expired or were set to expire had sought advice about seeking refugee protection in Australia.
"Clearly they are delegates that come from countries where to work in the AIDS field is a life-threatening proposition," Ms Curr said.
"It seems that some of them have been considering whether they think they can survive in their countries of origin, or whether they should try to survive by getting refugee protection in Australia."
The CEO of crisis accommodation service HomeGround, Heather Holst, said 14 of the delegates had sought her organisation's help to find shelter in Melbourne.
"Their situation is that they're in fear of returning and that they need somewhere to stay right now," Ms Holst said.
"We leave the seeking asylum and the legal position to the experts, but our piece is if anybody in Melbourne needs somewhere to stay, we'll try to help them with that."
The 20th International AIDS Conference wrapped up on July 25, after five days.
Australia offers 'intoxicating freedom': ASRC
Ms Curr said it was not unheard of for conference delegates to seek asylum in Australia.
"When people have come from countries where their daily lives are threatened by violence and politics, and they come to Australia and take a deep breath, walk down the street, and know that no one is going to kill them. It's a very intoxicating freedom," she said.
"We've had people in the past who have sought asylum and many of them have been granted asylum because their claims under the refugee protection are so strong.
"A refugee visa is one of the hardest visas to get in this country, you don't just get it easily, these people's claims will be assessed in line with the refugee convention and if they have a claim we hope that the government would extend them protection."