US-based International human rights lawyer Kimberley Motley, who is acting on behalf of Mr Yusufu, told SBS News that he was still in Doha but did not disclose whether he has been able to leave the airport.
She said Qatari officials originally allowed Mr Yusufu to have an extra 24 hours to find a country, but later extended that deadline to a couple of days.
"Right now we're just crossing our fingers and hoping we can figure out a country that is kind enough to accept this man," Ms Motley said.
"Otherwise I believe if he goes back to Beijing that he'll be persecuted. I think it's no secret how the Uighurs are being persecuted in China."
Ms Motely declined to elaborate on whether they were targeting any specific countries in order to obtain Mr Yusufu a visa on humanitarian grounds but Uighur-American advocate Salih Hudayar told SBS News he had attempted to reach out to Swedish authorities.
Sweden has pledged to grant refugee status to all Uighur asylum-seekers, whether or not they can prove they were fleeing persecution.
"[We] are working with other human rights organisations and NGOs to ensure that maximum pressure will be brought to bear on Qatar if they send this man to China, where he may face imprisonment, torture, or even death," Mr Hudayar said.
Executive Director of Human Rights Watch Kenneth Roth also called on Qatar to "respect its asylum obligations".
"The good news: under pressure, the Qatari government didn't force this Uyghur man, Abulikemu Yusufu, onto a flight this morning to persecution in China," he wrote on Twitter.
On Saturday, just hours before his flight to Beijing was scheduled to depart, Mr Yusufu made a desperate video from the airport begging for "the world's help".
The video, which was subtitled in English and posted on social media by Australian-Uighur human rights advocate Arslan Hidayat, led to a flood of support.
"He's OK, he feels a lot better than he did yesterday when he thought he was going to be deported," Ms Motley said.
"But he's still very anxious and very scared and he's hoping that he's pleas for help will be answered. And I think that social media is a wonderful, wonderful thing for human rights in a lot of ways."
The UN has estimated that more than one million Uighurs and other Muslim citizens are currently detained in Chinese camps throughout China's western Xinjiang region, with the remaining population subject to intense surveillance.
"Our goal is to have a compassionate country to open their doors to a very desperate man in a very desperate situation who just wants to be free and to live in a country where he won't be persecuted, where he won't be detained and where he can freely practice his religion," Ms Motley said.