But those with enough time served could stand to receive up to an extra £120.
In a heavily anticipated speech, Rachel Reeves, Labour's shadow work and pensions secretary, said she was "unequivocal" in wanting to strengthen the principle that those who pay more in should get more out of social security.
But she insisted increased payments to workers who lost their jobs should come at no extra cost to the taxpayer.
Labour sources later said one option under consideration included potential changes to contributory jobseeker's allowance.
At the moment workers pay National Insurance contributions to receive the benefit, which in some cases can be claimed alongside income-based jobseekers' allowance, if they become unemployed.
The contributory payments last six months and workers are eligible as long as they have paid in over two years. However, that threshold could rise to four or five years, sources said. This would allow workers to receive higher benefits without the policy costing any extra cash.
Ms Reeves insisted that no final details had yet been worked out.
"The direction I would like to go in is clear and what I would like to see is, if someone has contributed for four or five years for example...they might get a bit more in those first six weeks," she said. That could be "perhaps in the order of £20" a week, she added.
Ms Reeves also outlined plans to offer English, maths and IT classes to those out of work who needed them, with their benefits stopped if they failed to attend.
Welfare has emerged as a key battleground between Labour and the Conservatives ahead of the next general election, due in 2015 and Ms Reeve hit back at claims that she was copying the Conservatives, who have announced plans to pilot similar skills classes.
She accused the Tories of only testing whether or not people needed help after three years of being out of work.
Work and Pensions Secretary Iain Duncan Smith said: "This is typical of Labour - they haven't changed - it's the same old welfare party".
"Labour left our welfare system in a complete mess, with 1.4 million people spending most of the past decade on out-of-work benefits."