The game on 5 November is outside World Rugby's Test window and English clubs do not have to release players for it.
Gloucester flanker Ross Moriarty has said he expects to miss the match.
"As it stands, George will not be available for that game," Saints team manager Paul Shields said.
He told BBC Radio Northampton: "I know discussions are ongoing with the WRU and the [English clubs'] chairmen but I'm not privy to those conversations."
The decision to release England-based Wales internationals is now in the hands of Premier Rugby, the umbrella organisation for England's top-tier clubs.
Following the match against Australia, Wales face Argentina, Japan and South Africa later in the month - those Tests fall inside World Rugby's international window, which mean clubs must release their players.
The decision by Premiership clubs on whether to release players for the first match will also have ramifications for Harlequins centre Jamie Roberts and Bath's injured number eight Taulupe Faletau.
Earlier this week, Wales coach Rob Howley appeared to suggest North, Roberts and Faletau had special dispensation to play against the Wallabies.
However, Shields said: "George is no different than any other non-English player. There's no side letter that exists or anything in his contract that says we will release George to play.
"We're governed by Premier Rugby, who as a company will not release players outside the international window."
Meanwhile, Moriarty has said: "For the games after [Australia], I'll hope to be involved and have a good chance to play again."
Following fine performances for Wales during their summer tour in New Zealand, Moriarty has continued that form with Gloucester and received another call-up.
"Sometimes I've been left with my head in my hands worrying [about a call-up] but I had a conversation a couple of weeks ago and it was a pretty big hint," he told BBC Radio Gloucestershire.
"It's been on my mind for a while now. But as long as I can keep on performing and doing the best I can to help the team then that's what I'll keep on doing."

In 2003 there were around 1,596 pandas living in the wild, but according to the latest count there are now 1,864.
Nearly three quarters of the pandas live in China's south-western province of Sichuan.
The number of giant pandas in captivity has grown too - almost 200 more now than there were back in 2003.
Ginette Hemley, from animal charity World Wildlife Fund, says it's great news: "The rise in the population of wild giant pandas is a victory for conservation and definitely one to celebrate.''
But the latest count says the main threat to the panda numbers is the building of roads and power stations. Over 300 hydropower stations and 800 miles of roads have been built in areas where giant pandas live.

The so-called Immortal Regiment procession sees people carrying flowers and portraits of loved-ones.
It followed Russia's annual Victory Day parade, which marks the anniversary of the Soviet victory over Nazi Germany in World War Two.

Jason Roy hit 59 and Alex Hales 40, putting on 92 for the first wicket inside seven overs in Abu Dhabi.
Although the tourists faltered as they posted 174-6, the UAE managed only 95-9 in reply, with off-spinner Moeen Ali taking 4-11 and Chris Jordan 2-14.
The first T20 of the three-match series is in Dubai on Thursday at 16:00 GMT.
Eoin Morgan's side are building towards the World Twenty20 in India, which starts in March 2016.
Pakistan won the Test series 2-0 before England took the one-day series 3-1.
Wing George North is not currently available for Wales' Test against Australia but talks between the Welsh Rugby Union and English clubs are ongoing, his club Northampton says.
[NEXT_CONCEPT]
Good news for giant pandas - the number living in the wild in China has gone up over the last 10 years.
[NEXT_CONCEPT]
Tens of thousands of people have marched in Moscow and cities around the world to remember relatives who took part in World War Two.
[NEXT_CONCEPT]
England eased to a 79-run win over the United Arab Emirates in their only warm-up game before the Twenty20 series against Pakistan.