Djokovic, who is Serbian, was kicked out of Australia ahead of the Grand Slam in January after refusing to be vaccinated. The former world number 1 was originally banned from the country until 2025.
The ABC said it had confirmed the Immigration Minister Andrew Gilles had that ban overturned, allowing Djokovic to compete.
A spokesman for the Australian Department of Immigration declined to comment on the reports.
Australian Open tournament director Craig Tiley said this month Djokovic would be welcome in January if he could get a visa, but that Tennis Australia could not lobby for him.
Australia in July scrapped a rule requiring international travelers to declare their COVID vaccination status, and Djokovic said in October he had received “positive signals” about the status of efforts to reverse his ban.