They say the family are "wonderful contributors" to the community and are the type of people the city wants to attract.

READ MORE: Father's desperate plea: 'Please don't deport my family from Warrnambool to Singapore

Raj Manikam, his wife Premawathy and their children Vanisre, 18, and Vela, 8, are facing deportation on August 21 if they cannot obtain permanent residency status. The family's bid has been rejected because Mr Manikam has the early stages of kidney disease.

Cr Mike Neoh said they were a "model family" for the city.

"Warrnambool is signed up as a welcoming city and we have a number of strategies to attract skilled migrants," he said.

"This family went to a regional expo, saw Warrnambool, loved it and the council sponsored the family. They are great contributors to our city and they are exactly what we want. We have a welcoming, inclusive community."

He urged Wannon MP Dan Tehan to support the family to stay.

"We hope he will be very receptive to this case," he said. "I know he has provided a letter of support but we are really asking him to help us with this."

Cr Neoh's father Francis came from Malaysia years ago and raised his family in the city while running a popular restaurant.

Cr Kylie Gaston said for year 12 student and Brauer College school captain Vanisre it could not have come at a worse time.

"She is due to sit her VCE exams in 12 weeks," she said.

"She is a fantastic student and is in the youth choir and student well-being program. She is a young person contributing to our society in the very best of ways."

Thousands of people have signed a petition urging the governemnt to let the family stay.

You can sign the petition here.