Kathryn and Gregg Brain, who moved to Dingwall with their son Lachlan in 2011, are under pressure to leave the UK after failing to find work which would satisfy visa requirements.
They are due to meet lawyers in Glasgow tomorrow where they hope a position offered to Mrs Brain can be finalised.
The family moved to Scotland on Mrs Brain’s student visa five years ago, but a two-year post-study visa scheme then on offer was later withdrawn by the UK Government.
They have been living on handouts from friends in recent weeks and relied on a cheque from an anonymous benefactor to buy a new uniform for their son’s return to school.
Speaking yesterday, Mrs Brain said: “We just got a call from the lawyers that they had heard from the employer and they’re ready to go ahead.
“We just hope everything goes smoothly on Thursday and then we’ll be able to make an announcement soon after. Once all the paperwork is signed and submitted to the Home Office, I think everyone will be able to breathe a sigh of relief. We’re very optimistic Thursday will be a good day.”
UK immigration minister Robert Goodwill wrote to the family earlier this month saying there were “no exceptional considerations” that would justify granting them leave to remain outside of the immigration rules.
Mrs Brain said the family had received two phone calls from the Home Office’s family returns unit in Glasgow in the past week inquiring about their plans to return to Australia.
In order for the family to stay, either Mr or Mrs Brain is required to secure a skilled job, paying a minimum of £20,800 per year before they can make their visa application. The family have declined to provide details of the current job offer, but Mr Brain has previously said they were contacted by a “major Scottish company”.
Mrs Brain said: “We’ve been surviving on the continuing generosity of family, friends and church community.
“We got our boy back to school and I had to buy uniform for him. Just when we thought we weren’t going to be able to buy him a couple of pairs of trousers and two shirts, a cheque arrived in the mail.
“It’s just been quite amazing – it’s lovely. It brings a lump to our throat and tears to our eyes every time it happens. To know we have the community behind us is wonderful.”
She added: “The sooner I can begin work, the sooner we can begin paying our own way again.”
A Home Office spokesman said: “We have not received any fresh application from or on behalf of the Brain family which would allow them to stay in the UK. We have given the family three extensions on an exceptional basis over a number of months to allow them to try to secure a job that would allow them to meet the immigration rules, but this cannot be open-ended.
“In line with established policy designed to apply evenly and fairly to everyone, anyone who is unable to regularise their stay is expected to leave the UK voluntarily.”