The former world number one was due to travel to Australia on one of the charter flights laid on by tournament organisers but is still isolating at home.
The PA news agency 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 in Melbourne.
Murray and his team are working closely with tournament director Craig Tiley to try to come up with an acceptable solution.
Tournament organisers spent several months negotiating an arrangement that was acceptable to local and national government agencies regarding the admission of more than 1,000 tennis players and associated personnel to Australia.
A statement from the Australian Open did not appear to offer Murray too much hope, saying: “Andy Murray has advised that he has tested positive to Covid-19 and is isolating at home in the UK.
“Unfortunately this means he will be unable to join the official AO charter flights arriving in Australia in the coming days to go through the quarantine period with the other players.
“The AO fans love Andy, and we know how much he loves competing here in Melbourne and how hard he’d worked for this opportunity.”
Players began arriving in the country on Thursday ahead of a two-week period of quarantine, during which they are allowed out of their rooms to practise for five hours a day.
They were told that a positive test prior to flying would mean they were not allowed to travel to Australia.
Murray has been given a wild card for the tournament and is hoping to make his first appearance in Melbourne since the emotional events of 2019, when he revealed the extent of his right hip problems and raised the possibility of imminent retirement.
A resurfacing operation shortly afterwards allowed him to resume his career that summer but he has experienced several setbacks since, the most recent an issue with his left psoas muscle, which connects the spine to the femur.
He spoke positively about his fitness in November and last month played two matches at the most recent Battle of the Brits event, beating Dan Evans and Cameron Norrie.
World number 16 Madison Keys will not be making the trip after testing positive, with the American saying on Twitter: “I am self-isolating at home and will continue to follow all the necessary health precautions. I look forward to being back on tour next month.”
Meanwhile, tournament organisers have explained why American player Tennys Sandgren was allowed to travel to Australia despite testing positive for Covid-19 on Monday.
Sandgren, a two-time quarter-finalist in Melbourne, had coronavirus in November and is therefore no longer deemed infectious.
An Australian Open statement read: “In the case of Tennys Sandgren, who has self-disclosed that he previously tested positive in late November, his medical file had to be reviewed by Victorian health authorities. Upon completion of that review he was cleared to fly.”
Dominic Thiem’s coach, Nicolas Massu, has been unable to travel after testing positive but is hoping to fly at a later date while Carlos Moya, the coach of Rafael Nadal, has decided not to make the trip and will stay with his family.