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."
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.