The woman will find out this month whether the civil case can go ahead.
Her lawyer says a polygraph examination that she took in an effort to back her allegations could be used in the civil action at the Court of Session.
The woman's solicitor, Cameron Fyfe, said: "It would be a first. I don't think it's ever been done in a civil case before – it would be a new one. My client arranged the test privately."
He said a special hearing may be required to decide whether the test results could be considered, as polygraphs are currently inadmissible in Scottish civil and criminal courts.
"We would have to ask the court at the time of the final hearing if we could lead this evidence," he said. "Or, if the other side – Goodwillie's lawyers – think it's more appropriate, we could have a special hearing on that point alone. If the court says that, under Scots Law, it's not allowed, then that would be it."
He added: "I hope to have a decision on funding from the Scottish Legal Aid Board in the next two or three weeks."
Mr Fyfe said a successful action would leave Goodwillie facing damages of tens of thousands of pounds.
He said: "There is the pain and suffering of a victim and loss of earnings to take into account. The most severe examples of pain and suffering can result in damages of up to £40,000."
The woman accused Mr Goodwillie of raping her at a party. She claimed that her drink had been spiked.
Mr Goodwillie was charged with rape but never faced prosecution because the Crown Office ruled that there was insufficient evidence to proceed. Weeks later, the Criminal Injuries Compensation Authority decided the woman, a 25-year-old mother, had been raped and awarded her £11,000 compensation.
Liam O'Donnell, the lawyer representing Mr Goodwillie, said: "Based on the fact the woman had no memory of that evening beyond 10.30pm, we do not think there is any place in this case for a polygraph test."