The former treasurer ended speculation on a return to politics after draft redistribution changes shifted the margins of his old electorate, making Kooyong more winnable for the Liberals.
"Re the recent speculation about Kooyong: I am not rushing back to politics, my position on contesting the next election remains unchanged," he wrote on X.
"I will continue to support the Liberal Party and our local candidate Amelia Hamer."
Ms Hamer, 31, was pre-selected for the Melbourne seat in late March.
The Liberal Party is already under scrutiny for its lack of female parliamentarians.
Opposition finance spokeswoman Jane Hume had earlier talked down rumours of re-opening pre-selections based on draft boundary changes.
Senator Jane Hume says the former treasurer is a great supporter of women in parliament. (Lukas Coch/AAP PHOTOS)
"It would be a crazy thing to do," she told Sky News on Monday.
"I know that there's lots of people out there that would love to see Josh's return, but Josh is a great supporter of women in Parliament, always has been, and I know he's doing right by Amelia Hamer."
But former cabinet colleague Karen Andrews maintains the ex-treasurer should resurrect his political career.
"He would be an absolute asset to the team we take forward to the next election," she told ABC radio.
"(The Liberal Party) should do all they can to attract him back into our parliament and clearly if that means re-opening pre-selections then that has to be considered."
MP Karen Andrews says Josh Frydenberg 'would be an absolute asset' in the team at the next election. (Lukas Coch/AAP PHOTOS)
The Liberal Party's post election review found it had its lowest female representation in the new parliament in 30 years.
A number of Liberal parliamentarians have called for an increase in women being pre-selected.
Though the government has not announced an official date for the federal election, Australians will have to go to the polls by May 2025.
Ms Hamer has not directly addressed the rumours but on Sunday night  made a post about a local Kooyong woman who had won gold at the OWF International Elite Tournament.
Women can do anything! 💪� — Amelia Hamer (@HamerAmelia) Congrats to this amazing Kooyong local Eileen Cikamatana for taking out the gold medal in the OWF International Elite Tournament at Hawthorn Weightlifting Club today �Here in Kooyong the community loves to support strong women ���♀� pic.twitter.com/ADyJHtV8Y1June 2, 2024
"Here in Kooyong, the community loves to support strong women," she said.
Nationals leader David Littleproud said the party needed to pick the best candidate with the greatest shot of winning the seat.
"We don't believe in quotas, we believe you get there on on effort and on merit and who is the best person to win that seat whether they be male or female," he said
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