PA Consulting, which works with many of the leading carmakers and auto parts suppliers, then forecast sales for the period 2014-21, based on the company's insight into the various manufacturers' plans for electrification, engine optimisation and weight reduction.
Carmakers such as Renault, PSA Peugeot Citroën, Toyota and Fiat Chrysler Automobiles were found to be on-track to meet the fleet-average targets, while Hyundai, Ford, General Motors and Nissan were close to achieving the objectives.
But the three German brands and JLR were each set to miss the goals by 4g or more.
Were that trajectory to continue, the carmakers would face crippling fines of €95 for each gramme in excess of the target, multiplied by their annual sales in Europe. That means VW would face a fine of up to €1bn in the first year after the objectives are phased in.
"It's not so much they worry about the fine, it's more the damage to their reputation and prestige," said Thomas Göttle, the lead author of the report.
Driving with fewer emissions: how can carmakers meet the 2021 targets for CO₂ emissions?
The four carmakers declined to comment on the report as they had yet to review the details, though each stressed they were committed to meeting the targets.
VW has repeatedly pledged to reach the goals, and this month said it was investing more than any other manufacturer in new product technology. Martin Winterkorn, chief executive, said at last year's Paris motor show that every gramme of CO₂ reduction in its European fleet in Europe cost the group almost €100m a year.
BMW said it had new efficient models coming out soon, such as the large X5 plug-in hybrid this year, as well as further improvements to its gasoline and diesel variants.
JLR said it would seek to increase its use of light-weighting technologies, engine downsizing and hybridisation.
Daimler, owner of the Mercedes-Benz and Smart car brands, said that by 2017 it would have 10 plug-in hybrids in its portfolio.
"But the customer has to buy them," the Stuttgart-based company added. "It doesn't help us if we have brilliant hybrids in the showroom but the customer only buys V12 [engines]."
However Greg Archer, clean vehicles manager at Transport & Environment, said carmakers could drive down emissions with updated internal combustion engine technology and better aerodynamics. "This argument that they have to sell lots of electric vehicles to meet their targets is not borne out by the evidence," he said.