Mr Webb said at the weekend there could be ways to extend the pension freedoms to current annuity holders.
Mr Webb told The Sunday Telegraph retirees would be allowed to sell their annuities at any point to the highest bidder, generating what it described as a new market in second-hand annuities.
The paper reported Mr Webb saying pensioners had urged him to make the change, while some major pensions companies and insurers had also expressed "considerable interest and enthusiasm".
Two potential options would be, firstly, for the annuity income stream to continue but the annuity holder sells it to a third party in exchange for a lump sum.

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Secondly, the annuity holder and the insurance company could agree to cancel the contract, annuity payments cease and the investor could be paid a lump sum by their annuity provider.
Tom McPhail, head of pensions research at Hargreaves Lansdown, said: "It is to the government's credit that they are continuing to seek new ways to reinvigorate the retirement savings sector and to encourage investors to take control of their own money; we just don't think this latest idea will ever work.
"Similar schemes using life insurance contracts in the past were labelled by the FSA as 'high risk, toxic products."
He said: "There is an obvious appeal in finding a way to extend the pension freedoms to existing annuity holders, giving them the option to take their money back as a lump sum if they want.
"There is overwhelming support for the new pension rules and with an election looming, unlocking these existing contracts would be a vote winner."
He added though that those who would have to carry out this work, if the idea was to go ahead, would be the same insurers, actuaries and pension companies already "working flat out" to deal with all the other pension changes coming in. 

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