Mr Frydenberg used an interview to criticise Mr Taylor's handling of the party, saying the current leader had contributed to Liberal polling being at an "all-time low".
"Things have to change, because there's something existential about the threat that I think the party now faces," he told Nine's 60 Minutes.
"(Mr Taylor is) getting (criticism) from lots of corners. People are saying that the Liberal Party needs to do better."
Excerpts from Mr Frydenberg's memoir, which is likely to contain policy suggestions, have fuelled rumours that he is planning to make a political comeback.
"Look, I certainly haven't closed the door, but I don't need to rush to a decision. The next election is 18 months away," he said.
Despite the criticism, Mr Taylor said his former Liberal colleague would be welcomed back into the fold should he decide to run.
"I welcome every Liberal who cares about the future of our nation - and I know Josh does - to put shoulder to the wheel in the coming months to get rid of a rotten Labor government and make the change that Australia needs happen," he told reporters in Canberra on Monday.
"I ask all Liberals and Nationals and people who are supportive of our view about where the country needs to go … to get in there and help in any way they can."
Mr Frydenberg held the seat of Kooyong for 12 years from 2010 and was treasurer in the Morrison government, including through COVID-19.
He lost the seat to independent MP Monique Ryan at the 2022 election, in which she won almost 53 per cent of the two-party preferred vote.
Dr Ryan appeared unfazed by her competition's possible return.
"I'm not bothered either way," she told Nine's Today program.
"Josh does have a track record with the Kooyong community.
"He was the member for that seat for 12 years, and in 2022, our community rejected him because they were so frustrated with his inability to affect any change to government policy on climate change.
"People were unhappy with his economic management."
Shadow treasurer Tim Wilson encouraged people to "put themselves forward" as candidates to create a stronger Liberal Party.
"I encourage them to do so, so they can be part of a winning team. So we can have an Angus Taylor-led government," he told ABC Radio.
"What we need is people who've got courage in their hearts and are prepared to make the sacrifices necessary for public office."
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