Labour intends to allow as many as 80,000 young Europeans to reside and work in Britain each year, marking a new Brexit concession to the EU.
Ministers have lifted the proposed limit from 50,000 in an effort to clinch an agreement before Andy Burnham's EU summit on 20 November.
The scheme would permit EU citizens aged 18 to 30 to stay, work and study in the UK for a period of up to three years.
According to The Sunday Times, Brussels is asking for a higher ceiling of 100,000 spots.
Shadow Home Secretary Chris Philp criticised the move, saying: "At a time when young Brits are struggling to find jobs, afford housing and get on the property ladder, Labour is putting the interests of the EU ahead of our own people.
"This is not a reset; it is a retreat.
"Meanwhile thousands continue to cross the Channel illegally and Labour look set to water down reforms to ILR. The Conservatives are the only party that will secure our borders and put our national interest first."
EU negotiators are also pressing for reduced university fees for European students, even though officials warn the proposal could cost financially strained British universities millions.
The government hopes to reach deals on youth mobility, reduce border checks on food exports, and align emissions trading schemes at the summit.
Significant obstacles remain, casting doubt on whether a pact can be finalised in time.
Burnham is also set to present options for Britain's future relationship with the EU later this month, after admitting he hopes to see the country re-join the bloc in his lifetime.