Australian officials have hinted that Alqunun's request is likely to succeed.
Thai authorities arrested and charged AlAraibi, a Bahraini footballer who has a refugee status in Australia, late a year ago. The 18-year-old was stopped by officials in Thailand who confiscated her passport.
This handout picture taken and released by the Thai Immigration Bureau shows Qunun (right) being escorted by a United Nations High Commissioner for Refugees (UNHCR) official at Suvarnabhumi worldwide airport in Bangkok. "If I go back to Saudi Arabia, I will be dead".
But Rahaf Mohammed al-Qunun's father and brother would have to wait and see whether the United Nations refugee agency would allow them to see her, immigration chief Surachate Hakpan said. "The Saudi charge d'affaires said he is satisfied and expressed confidence on the work of Thai immigration, of the Thai government, and of the Foreign Ministry yesterday".
"She does not wish to go back and we will not force her".
Rahaf Mohammed Alqunun, 18, plotted an escape from what she describes as persistent abuse and oppression by family members in Saudi Arabia.
"The government has said that promoting women's rights is a priority as part of its foreign policy; well here's a concrete case where they can protect a young woman's life, and the government should be seizing that opportunity and making its views widely known".
Three dead in double-decker bus crash at busy Ottawa transit station
The driver of the bus was "detained on the scene and will be questioned at our police station", Bordeleau said. He was in his apartment across the street from the station when he started hearing sirens just after 4 p.m.
In 2017, Dina Lasloom triggered an online firestorm when she was stopped en route to Australia where she planned to seek asylum.
On Sunday, Thai immigration chief Surachate Hakparn made a statement that Qunun was denied entry because of her lack of documents. Those women and the men who are fighting for women's rights activists who are in prison today in Saudi Arabia, they are the leaders - the vanguard of a revolution that will free Saudi women... by ending once and for all the guardianship system which is the foundation of patriarchy in Saudi Arabia...
Ms Al-Qunun said her male guardian had reported her for travelling "without his permission".
"What is truly appalling is how the Saudi Arabian government has acted in sending an official to physically seize her passport from her in Bangkok airport global transit", Mr Robertson said.
Global pressure has mounted on Thai authorities to keep Alqunun safe and to ensure she isn't forcibly returned to the Saudi kingdom, which has been subject to worldwide condemnation over the killing of Washington Post writer Jamal Khashoggi at a Saudi consulate in Turkey. Thai immigration authorities have said that al-Qunun was prevented from onward travel to Australia, having been in contact with the "Saudi Arabia embassy to coordinate" this. It said the embassy is not communicating with the teenager, but is communicating with Thai authorities.
"[Ms] Rahaf is not a political asylum case", he insisted.
Women trying to escape abuse by their families have been caught trying to seek asylum overseas in recent years and returned home.
Alqunun's shrewd use of social media - one of the few tools available to her while barricaded in a hotel room - may have been her saving grace.
Saudi Arabia's human rights record has come under intense scrutiny since the killing of Saudi writer Jamal Khashoggi in October.