At present, the UK government, like others, issues bonds - a form of IOU - which pay interest before being paid back after a fixed term.
A long-dated bond typically gives the government 30 years to repay, but these new bonds may be for 100 years or more.
However, pension funds have suggested there may be little demand for them.
"A 100-year bond would be too long for most pension funds, and we don't think that many would buy them," said Joanne Segars, chief executive of the National Association of Pension Funds (NAPF), whose members are major investors in UK government bonds.
"Most final-salary pension schemes are now closed to new joiners and are becoming more mature. Their liabilities are long-term, but not that long-term.
"Pension funds are looking for 30, 40 and 50-year index-linked debt, and would much rather the government issue more of those."
The new plan is looking at issuing bonds with a 100-year repayment date, or even longer.
In his Budget next week, Chancellor George Osborne will announce that he will consult on creating a new "super-long" gilt that could even be issued with no set redemption date.
The theory is that these super long-term gilts would allow the government to lock in the current record low interest rate for a very long time.
If the bond proved popular with investors, future governments would pay less debt interest for years to come.
But the BBC's business editor Robert Peston questioned the appetite for such long-term debt.
"There are few obvious natural buyers for 100-year or perpetual bonds," he said.
"The main purchasers of long-term debt are final-salary pension schemes and life companies. But both venerable British savings institutions are in decline in the UK."
Labour's shadow chief secretary to the Treasury, Rachel Reeves, said the government's "failed policies", meant it was having to borrow £158bn more than planned.
"This is not extra borrowing to help build a stronger economy for the future, but to pay for the costs of economic failure and the bills of a growing dole queue.
"Britain already has more long-term debt than other countries but we will look hard to see if this proposal actually delivers value for money for the taxpayer."
Treasury officials described the plan as like the country taking out a low-rate fixed-term mortgage.
They said official figures reveal that the low cost of long-term interest rates will save the country £20bn in debt interest over the next five years.
BBC political editor Nick Robinson said the Treasury estimated this was worth approximately £1,000 for every UK household.
There are currently eight of these perpetual gilts in existence worth some £2bn - with the oldest dating back to 1853.
The last perpetual loan was taken out to cover the cost of World War I. The 1932 war loan has an implicit interest rate of 3.9% at its current price.
The chancellor is accompanying Prime Minister David Cameron on his trip to the US where he will have meetings with his US counterpart Timothy Geithner and head of the IMF Christine Lagarde.
Officials travelling with him say that next week's Budget has still not been finalised.
There will be another meeting of the coalition's governing "quad" on Friday.
The quad is the name given to meetings of the prime minister and chancellor from the Conservative side and the deputy prime minister and the chief secretary to the Treasury from the Liberal Democrat side.
One source said "things are still moving around" but insisted that many issues had been resolved.
The Treasury has to inform the independent Office for Budget Responsibility of its key tax and spending decisions by the end of Friday so that the OBR can factor them in to its economic forecasts.
The Treasury is expected to spell out the details of its credit easing plan - to underwrite loans for small businesses - next Monday, ahead of the Budget on 21 March.