The former world number one had been due to travel to Australia on one of the 18 charter flights laid on by tournament organisers but is stuck isolating at home.
ITV News understands that Murray - who is said to be in good health - is hoping to be able to arrive in Australia at a later date and participate in the year’s first grand slam, which begins on February 8.
Murray and his team are working closely with tournament director Craig Tiley to try to come up with an acceptable solution.
Organisers of the tournament have spent months negotiating arrangements with Australia's national government and local leaders in order to get more than 1,000 tennis players and associated personnel into the country.
Players are due to begin arriving in Australia within the next 24 hours before completing a two-week period of quarantine.
The plan is to allow players out of their rooms to practise for five hours a day.
Players had been told that a positive Covid test prior to flying would mean they were not allowed to travel to Australia.
Last year's men's singles winner, Novak Djokovic, tested positive for Covid in June 2020 in the wake of the Adria Tour events he helped organise in Serbia and Croatia.
While other flagship events in the tennis calendar - including Wimbledon - fell victim to the disruption of the first wave of coronavirus.
The Australian Open 2020 hit the headlines after poor quality in the area impacted a number of players, following massive wildfires in the country.