"If I get elected as prime minister on Saturday, I will ask my immigration spokesperson to review the matter because community sentiment matters," Mr Shorten said.
The tight-knit town of Biloela has been holding regular protests for their former neighbours around the country.
"If a community wants some people to live with them, why are we all making it so hard for that outcome?" the opposition leader said.
"This family, as I understand, has exhausted a range of legal appeals. It's right back on the minister's desk."
He said if Biloela "wants to keep this precious family in their community, I think that's a good idea, not a bad idea".
"I'm promising to reopen the matter and I'm promising to give it consideration."
The couple came to Australia separately by boat in 2012 and 2013 following Sri Lanka's civil war, but have been in detention in Melbourne since March 2018 after their bridging visa expired.
Supporters of the family say they would face persecution in their native Sri Lanka because of past family links to the banned Liberation Tigers of Tamil Eelam.
The Tamil Tigers separatist group were proscribed as a terrorist group by 32 countries during their insurgency against the Sri Lankan government. The militants were effectively defeated in 2009, after 26 years of bloody conflict.
In the dying days of the election campaign supporters of the family will travel to Immigration Minister David Coleman's marginal Sydney electorate of Banks to ask him to intervene in the case and keep them in Australia.
About 400 supporters will rally in Melbourne on Wednesday to highlight the family's value to the community and raise concerns about returning them to Sri Lanka, where Priya's ex-fiance and five other men were burned to death before her eyes.
"We're really fearful they could be deported any moment ... so we're just praying that if we're in his seat of Banks and we create enough buzz he can't ignore us," supporter Angela Fredericks told AAP.
Former Socceroo joins the fight
She said former Socceroo Craig Foster who campaigned to free refugee footballer Hakeem al-Araibi from a Thai prison will help present a 189,000-signature petition calling for the family's release to Mr Coleman's office on Friday.
That's if supporters of the family from the tiny central Queensland town of Biloela don't manage to catch the minister earlier on the election trail.
Foster says he was committed to changing the immigration policy to better reflect the basic rights of vulnerable people, in line with international legal standards.
"Other countries, like our neighbours across the ditch, have demonstrated that a country is perfectly capable of caring for people and the Australians I know and love want us to take the lead in this area, not keep bringing up the rear," he said.
"The family has made a social contribution already, which is what's asked of them; the kids are part of the local school and unsurprisingly are suffering health problems in detention.
"Does Australia really need to be a place that detains two young girls behind barbed wire, without upholding their right to education, and to deny their community values members and for what purpose other than meanness of spirit?"
A spokesman for Mr Coleman said he would not comment on specific cases.
Former Australian Human Rights Commission president Gillian Triggs says the minister has the power to grant a visa to someone when it's in the public interest.
But on Tuesday, Sri Lankan Consul General to Australia Lal Raj Wickrematunga told SBS News it was "safe" for the family to return.
"As far as the Sri Lankan government is concerned, Sri Lanka is safe for Tamil families to return.
"The government has made an appeal for all those who’ve left Sri Lanka and sought refugee status elsewhere to come back."
And a spokesperson for Australian Border Force said the case had been thoroughly assessed.
"This family's case has been assessed, over many years, by the Department, various tribunals and courts … non-citizens who do not hold a valid visa and who have exhausted all outstanding avenues to remain in Australia are expected to depart," the spokesperson said.
Concerns for the family's children were raised earlier this month by the Victorian children's commissioner Liana Buchanan.
A medical report and photos obtained by the Ms Buchanan, detailed deterioration in health, particularly the dental health, of the girls.
Blackened front teeth, understood to belong to two-year-old Tharnicaa, were highlighted in the report.
"When I see that photo I am incredibly distressed. I think everybody would be. And the idea that in a country like Australia, a well-resourced country and we think of ourselves as fairly civilised," Ms Buchanan told SBS News earlier this month.
The report also noted both sisters have developed behavioural issues as a result of the environment, deemed "not appropriate" for young children.
In particular, the report noted the lack of social interaction with other children and restrictions on freedom of movement.
"There is no playgroup or early childhood learning in place," the report states.