Mr Scholz’s pitch includes putting a price on carbon, revamping industry and striking deals with developing countries to help them rid their economies of greenhouse gases.
The idea of a common carbon price is that countries can go green without being undercut by potentially polluted goods from abroad — leaving the world's emissions no better off, in what is known as carbon leakage.
And the hope is that consensus on climate issues will be easier to find in an alliance of like-minded countries than in existing forums with chronic political differences, such as the G20 or the United Nations.
Germany’s plan won public backing on Sunday of the European Union, whose council president Charles Michel said a climate club could limit carbon leakage and complement the 192-country Paris Agreement.
“This is needed if we want to be serious,” said Mr Michel, who said a climate club could help the world go beyond “nice declarations and statements” into concrete action.
The G7 discussed the proposal at the first of seven working sessions in Germany. An EU official said the negotiations were progressing well and that leaders saw the club as a good idea.
They are expected to make a stand-alone announcement endorsing the principle of a climate club at the end of the summit, although some questions are likely to remain open such as how to measure the effectiveness of vastly different climate policies.
Mr Scholz, who first floated the idea when he was a member of former chancellor Angela Merkel’s cabinet, wants the club to join forces to clean up the steel industry and set common standards for green hydrogen.
He has compared the idea to the G20’s move last year to establish a minimum corporate tax, a proposal championed by Mr Scholz when he was finance minister.
Diplomats have described carbon pricing as the trickiest issue in the G7 climate talks, with the US yet to embrace the concept at home, and said the negotiations could continue until the 11th hour.
The proposal has drawn a guarded response from climate activists, who say the idea is not a bad one in principle but cannot become a talking shop that stalls concrete commitments.
Friederike Meister, the director of advocacy group Global Citizen, told The National the idea as described by Mr Scholz was still too vague to assess properly.
However, a climate club “does not work without other measures”, such as more money for developing countries and compensation for environmental damage, she said.
The Fridays for Future movement said a climate club would be "just for show" if Mr Scholz's government keeps buying more natural gas and equivocating on banning petrol cars.
Activists say much would depend on the membership of such a club. Mr Scholz has said the G7 countries should “form the nucleus” but that it would be open to any country prepared to sign up to minimum standards.
South Africa last year signed up to a blueprint with some of the G7 powers to clean up its power grid with $8.5 billion of western money.
German officials are staying quiet on reports that a similar plan is envisaged for India but Mr Michel said the EU was ready to engage with any country “prepared to take real action” on decarbonising industry.
Climate protesters staged a show of strength on Sunday in Garmisch-Partenkirchen, a ski town where demonstrators are being held at arm’s length from the G7 venue.
Police said they had broken up a rally after fireworks were set off in the town.