The government is reported to be considering new rules that would allow existing annuity holders to sell their plans in return for a cash lump sum.
The idea is being championed by pensions minister Steve Webb and Ros Altmann, the government's older workers' advocate. A consultation could be announced in next week's Budget.
Until the introduction of the new pensions freedoms - coming into force on 6 April - many retirees have had little choice but to buy an annuity with their pension, even it represented poor value.
Ros Altmann said: "I have heard from so many people who are furious that they had to buy their annuity in the past couple of years, whereas if they had been younger the new rules would have meant they could have avoided locking all their pension savings into a product they did not want."
Among the retirees that could benefit are those that need a lump sum for urgent spending needs such as paying off debts or for care. Likewise those policyholders whose annuities are only paying a matter of pounds a week may find they can make better use of a lump sum.
While you might not be happy with your annuity, selling it would not be without risk. By taking the money now and spending it you are stripping yourself of future income.
Tom McPhail, head of pensions research at Hargreaves Lansdown, said: "For a minority of existing annuity investors this idea could make sense. However, there are likely to be significant costs and risks involved and these may well outweigh any potential benefit."
While selling back an annuity may not make monetary sense, Altmann says it is important that people who have already retired and purchased annuities are given the same freedoms as those retiring after April.
"This is an idea worth pursuing and could help so many people who are currently stuck in an annuity that they never wanted to buy. It is only an option, and unlike the past rules that forced people to lock their pension savings into a potentially unsuitable or poor value product that did not meet their needs, it gives them the chance to choose what they want to do"
It is as yet unclear how annuity holders would sell their policy. One option would be for insurers to buy back the policy, alternatively a market for second-hand annuities could be established.
Tom McPhail said: "In theory, a broker market could be created for existing annuity contracts, with buyers bidding to purchase the existing income stream from the annuitant. It is unclear who would want to buy such an investment from the annuity holder."
In either instance, the cash sum the annuity holder receives in return for their policy is highly likely to be worth less than the remaining value of the plan.