The proposal is stoking anger in Brussels, where Germany's negotiating tactics are regarded as heavy-handed.
The latest compromise would allow a phase-in of a 95 grams per kilometre (g/km) limit on auto carbon dioxide emissions until 2022 and increase the number of supercredits, a mechanism that gives companies more flexibility, the diplomats said.
Supercredits allow manufacturers that make very low emission vehicles, such as electric vehicles, to claim extra credit for them, so that they can continue to produce more heavily polluting vehicles as well.
A spokeswoman for Lithuania said the EU presidency was holding consultations on a possible compromise, which environment ministers had said should allow "limited additional flexibility".
A closed-door meeting is expected today (30 October) followed by talks with the European Parliament next week.
One diplomat predicted that an eventual deal could involve a two-year phase-in that would benefit all manufacturers across Europe, without the extra supercredits.
As irritation has mounted against Germany following months of intense lobbying, nations such as Italy and France will be reluctant to hand the competitive advantage of supercredits to Germany, the diplomats said.
German automakers have big plans for electric cars, such as BMW's i3 and fuel cell vehicles, while BMW and Daimler also continue to turn out a luxury fleet of high-performance, high-profit, fuel-intensive cars.
"I understand the need for Germany to protect its industry, but basically this is just the interests of two German companies, and the consequences are quite extreme," one diplomat said on condition of anonymity.
Pressure from the top
Chancellor Angela Merkel has taken up the cause of the big German carmakers, declaring she was protecting German jobs, and persuaded other EU states to agree to tear up an agreement on 2020 emissions targets that was reached in June.
Once a political deal has been struck after months of EU negotiations, it is unheard of for member states to agree to start all over again.
States such as Denmark, Britain and Sweden said any new deal had to be agreed quickly and must maintain "environmental integrity".
EU diplomats and campaign groups said the latest proposal would be negative for the environment and for consumers who want to burn less fuel.
Researchers at British-based consultancy Cambridge Econometrics found that the European Union would save €70 billion per year on oil imports if the 95 g/km target were implemented across its fleet.
Campaign group Transport & Environment said the new proposal, including all the supercredits, could effectively result in a four-year delay of the 2020 target. It called on EU member states and the European Parliament to reject it.
So far Europe has a 2015 CO2 limit of 130 g/km as an average across the EU fleet, a goal many manufacturers are already meeting or very close to doing so.