British bank Barclays could issue up to 7 billion pounds ($11 billion) in so-called contingent convertibles, or CoCos, people close to the matter said on Monday, adding to the 3 billion it raised in November.
The bank could ask for shareholder approval at its annual meeting on April 25, said a source, who declined to be named because proposals for the meeting have not been finalised.
Meanwhile, 82 percent government-owned RBS will this week flag it could issue CoCos.
While RBS has previously steered clear of the hybrid financial instruments whose value has elements of debt and equity, the Financial Services Authority - Britain's financial watchdog - has been encouraging banks to build capital buffers through CoCos, a source close to the situation said.
If banks want to issue a significant amount of CoCos, which convert into shares when their core capital ratio falls below a certain level, they need shareholder approval because it could be dilutive for existing shareholdings.
Barclays and RBS declined to comment.
How the banks structure any deals is unclear - there is no standard structure for CoCos.
Barclays may prefer to stick with the structure used in November, selling bonds whose value is written down to zero - rather than being converted into shares - if its core capital ratio falls below 7 percent.
Lloyds Banking Group sold 10 billion pounds of convertible bonds as part of a 25 billion pound recapitalisation plan in 2009. A high-profile hedge fund said last year the bonds were "expensive and uneconomic", underlining the wariness of mainstream investors about hybrid securities.
The FSA took a hard line on the structure of the deal by Barclays in November, requiring a "high trigger" to ensure it will rebuild capital early if its balance sheet deteriorates.
Chief executive Antony Jenkins told analysts when he set out his strategy two weeks ago he planned to build contingent capital "over the next few years" and expected loss-absorbing capital instruments to cover about 2 percent of the bank's risk-weighted assets (RWAs).
RWAs are assets, usually loans, adjusted for the likelihood of non-payment, and are a key determinant of a bank's capital requirements.
Jenkins expects RWAs to be about 440 billion pounds in 2015, implying contingent capital needs of 9 billion pounds.
The Sunday Telegraph newspaper reported that Barclays would sell up to 3 billion pounds of CoCos in May if it got approval from shareholders.
The greater risk attached to CoCos comes at a cost. Barclays is paying 7.625 percent interest on the 10-year bonds issued in November. That offer attracted $17 billion of demand, despite concern that the high trigger level would deter buyers.