The High Court has refused to hear an appeal on behalf of a four-year-old girl whose Tamil family are fighting to avoid deportation and return home to the Queensland town of Biloela.

The litigation guardian of Tharnicaa Murugappan had sought special leave to appeal to the nation's highest court, but that was declined on Thursday.

Earlier this year the full bench of the Federal Court upheld a judge's ruling that Tharnicaa had been denied procedural fairness when trying to apply for a protection visa to stay in Australia.

However, the court also upheld a judgement that Tharnicaa had not made a valid visa application back in 2019 and the family sought to challenge that in the High Court.

In June Immigration Minister Alex Hawke granted three-month bridging visas to Tharnicaa's father Nades, mother Priya and older sister Kopika, who like Tharnicaa was born in Australia.

Mr Hawke said at the time his decision allowed the three family members to live in Perth "while the youngest child's medical care, and the family's legal matters, are ongoing" and that Tharnicaa's "visa status is unchanged".